Factors of 999,999,999,840. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 999,999,999,840. Connection with the prime factorization of the number

Calculations:

Calculate all the (common) factors (divisors) of one or two numbers

To find all the divisors of the number 999,999,999,840:

1. Decompose the number into prime factors.
See how you can find out how many factors (divisors) the number has, without actually calculating them.
2. Multiply the prime factors in all their unique combinations, that yield different results.

1. Carry out the prime factorization of the number 999,999,999,840:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

999,999,999,840 = 2⁵ × 3 × 5 × 71 × 733 × 40,031
999,999,999,840 is not a prime number but a composite one.

Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
Examples of prime numbers: 2 (factors 1, 2), 3 (factors 1, 3), 5 (factors 1, 5), 7 (factors 1, 7), 11 (factors 1, 11), 13 (factors 1, 13), ...
Composite number: a natural number that has at least one factor other than 1 and itself. So it is neither a prime number nor 1.
Examples of composite numbers: 4 (it has 3 factors: 1, 2, 4), 6 (it has 4 factors: 1, 2, 3, 6), 8 (it has 4 factors: 1, 2, 4, 8), 9 (it has 3 factors: 1, 3, 9), 10 (it has 4 factors: 1, 2, 5, 10), 12 (it has 6 factors: 1, 2, 3, 4, 6, 12), ...
» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers (decomposition into prime factors)

How to count the number of factors of a number?

Without actually finding the factors

If a number N is prime factorized as:
N = a^m × b^k × c^z
where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, ....
...
Then the number of factors of the number N can be calculated as:
n = (m + 1) × (k + 1) × (z + 1)
...
In our case, the number of factors is calculated as:
n = (5 + 1) × (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 6 × 2 × 2 × 2 × 2 × 2 = 192

But to actually calculate the factors, see below...

2. Multiply the prime factors of the number 999,999,999,840

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.
Also consider the exponents of these prime factors.
Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.

All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

Numbers other than 1 that are not prime factors are composite factors (divisors).

neither prime nor composite = 1

prime factor = 2

prime factor = 3

composite factor = 2² = 4

prime factor = 5

composite factor = 2 × 3 = 6

composite factor = 2³ = 8

composite factor = 2 × 5 = 10

composite factor = 2² × 3 = 12

composite factor = 3 × 5 = 15

composite factor = 2⁴ = 16

composite factor = 2² × 5 = 20

composite factor = 2³ × 3 = 24

composite factor = 2 × 3 × 5 = 30

composite factor = 2⁵ = 32

composite factor = 2³ × 5 = 40

composite factor = 2⁴ × 3 = 48

composite factor = 2² × 3 × 5 = 60

prime factor = 71

composite factor = 2⁴ × 5 = 80

composite factor = 2⁵ × 3 = 96

composite factor = 2³ × 3 × 5 = 120

composite factor = 2 × 71 = 142

composite factor = 2⁵ × 5 = 160

composite factor = 3 × 71 = 213

composite factor = 2⁴ × 3 × 5 = 240

composite factor = 2² × 71 = 284

composite factor = 5 × 71 = 355

composite factor = 2 × 3 × 71 = 426

composite factor = 2⁵ × 3 × 5 = 480

composite factor = 2³ × 71 = 568

composite factor = 2 × 5 × 71 = 710

prime factor = 733

composite factor = 2² × 3 × 71 = 852

composite factor = 3 × 5 × 71 = 1,065

composite factor = 2⁴ × 71 = 1,136

composite factor = 2² × 5 × 71 = 1,420

composite factor = 2 × 733 = 1,466

composite factor = 2³ × 3 × 71 = 1,704

composite factor = 2 × 3 × 5 × 71 = 2,130

composite factor = 3 × 733 = 2,199

composite factor = 2⁵ × 71 = 2,272

composite factor = 2³ × 5 × 71 = 2,840

composite factor = 2² × 733 = 2,932

composite factor = 2⁴ × 3 × 71 = 3,408

composite factor = 5 × 733 = 3,665

composite factor = 2² × 3 × 5 × 71 = 4,260

composite factor = 2 × 3 × 733 = 4,398

composite factor = 2⁴ × 5 × 71 = 5,680

composite factor = 2³ × 733 = 5,864

composite factor = 2⁵ × 3 × 71 = 6,816

composite factor = 2 × 5 × 733 = 7,330

composite factor = 2³ × 3 × 5 × 71 = 8,520

composite factor = 2² × 3 × 733 = 8,796

composite factor = 3 × 5 × 733 = 10,995

composite factor = 2⁵ × 5 × 71 = 11,360

composite factor = 2⁴ × 733 = 11,728

composite factor = 2² × 5 × 733 = 14,660

composite factor = 2⁴ × 3 × 5 × 71 = 17,040

composite factor = 2³ × 3 × 733 = 17,592

composite factor = 2 × 3 × 5 × 733 = 21,990

composite factor = 2⁵ × 733 = 23,456

composite factor = 2³ × 5 × 733 = 29,320

composite factor = 2⁵ × 3 × 5 × 71 = 34,080

composite factor = 2⁴ × 3 × 733 = 35,184

prime factor = 40,031

composite factor = 2² × 3 × 5 × 733 = 43,980

composite factor = 71 × 733 = 52,043

composite factor = 2⁴ × 5 × 733 = 58,640

composite factor = 2⁵ × 3 × 733 = 70,368

composite factor = 2 × 40,031 = 80,062

composite factor = 2³ × 3 × 5 × 733 = 87,960

composite factor = 2 × 71 × 733 = 104,086

composite factor = 2⁵ × 5 × 733 = 117,280

composite factor = 3 × 40,031 = 120,093

composite factor = 3 × 71 × 733 = 156,129

composite factor = 2² × 40,031 = 160,124

composite factor = 2⁴ × 3 × 5 × 733 = 175,920

composite factor = 5 × 40,031 = 200,155

composite factor = 2² × 71 × 733 = 208,172

composite factor = 2 × 3 × 40,031 = 240,186

composite factor = 5 × 71 × 733 = 260,215

composite factor = 2 × 3 × 71 × 733 = 312,258

composite factor = 2³ × 40,031 = 320,248

composite factor = 2⁵ × 3 × 5 × 733 = 351,840

composite factor = 2 × 5 × 40,031 = 400,310

composite factor = 2³ × 71 × 733 = 416,344

composite factor = 2² × 3 × 40,031 = 480,372

composite factor = 2 × 5 × 71 × 733 = 520,430

composite factor = 3 × 5 × 40,031 = 600,465

composite factor = 2² × 3 × 71 × 733 = 624,516

composite factor = 2⁴ × 40,031 = 640,496

composite factor = 3 × 5 × 71 × 733 = 780,645

composite factor = 2² × 5 × 40,031 = 800,620

composite factor = 2⁴ × 71 × 733 = 832,688

composite factor = 2³ × 3 × 40,031 = 960,744

This list continues below...

... This list continues from above

composite factor = 2² × 5 × 71 × 733 = 1,040,860

composite factor = 2 × 3 × 5 × 40,031 = 1,200,930

composite factor = 2³ × 3 × 71 × 733 = 1,249,032

composite factor = 2⁵ × 40,031 = 1,280,992

composite factor = 2 × 3 × 5 × 71 × 733 = 1,561,290

composite factor = 2³ × 5 × 40,031 = 1,601,240

composite factor = 2⁵ × 71 × 733 = 1,665,376

composite factor = 2⁴ × 3 × 40,031 = 1,921,488

composite factor = 2³ × 5 × 71 × 733 = 2,081,720

composite factor = 2² × 3 × 5 × 40,031 = 2,401,860

composite factor = 2⁴ × 3 × 71 × 733 = 2,498,064

composite factor = 71 × 40,031 = 2,842,201

composite factor = 2² × 3 × 5 × 71 × 733 = 3,122,580

composite factor = 2⁴ × 5 × 40,031 = 3,202,480

composite factor = 2⁵ × 3 × 40,031 = 3,842,976

composite factor = 2⁴ × 5 × 71 × 733 = 4,163,440

composite factor = 2³ × 3 × 5 × 40,031 = 4,803,720

composite factor = 2⁵ × 3 × 71 × 733 = 4,996,128

composite factor = 2 × 71 × 40,031 = 5,684,402

composite factor = 2³ × 3 × 5 × 71 × 733 = 6,245,160

composite factor = 2⁵ × 5 × 40,031 = 6,404,960

composite factor = 2⁵ × 5 × 71 × 733 = 8,326,880

composite factor = 3 × 71 × 40,031 = 8,526,603

composite factor = 2⁴ × 3 × 5 × 40,031 = 9,607,440

composite factor = 2² × 71 × 40,031 = 11,368,804

composite factor = 2⁴ × 3 × 5 × 71 × 733 = 12,490,320

composite factor = 5 × 71 × 40,031 = 14,211,005

composite factor = 2 × 3 × 71 × 40,031 = 17,053,206

composite factor = 2⁵ × 3 × 5 × 40,031 = 19,214,880

composite factor = 2³ × 71 × 40,031 = 22,737,608

composite factor = 2⁵ × 3 × 5 × 71 × 733 = 24,980,640

composite factor = 2 × 5 × 71 × 40,031 = 28,422,010

composite factor = 733 × 40,031 = 29,342,723

composite factor = 2² × 3 × 71 × 40,031 = 34,106,412

composite factor = 3 × 5 × 71 × 40,031 = 42,633,015

composite factor = 2⁴ × 71 × 40,031 = 45,475,216

composite factor = 2² × 5 × 71 × 40,031 = 56,844,020

composite factor = 2 × 733 × 40,031 = 58,685,446

composite factor = 2³ × 3 × 71 × 40,031 = 68,212,824

composite factor = 2 × 3 × 5 × 71 × 40,031 = 85,266,030

composite factor = 3 × 733 × 40,031 = 88,028,169

composite factor = 2⁵ × 71 × 40,031 = 90,950,432

composite factor = 2³ × 5 × 71 × 40,031 = 113,688,040

composite factor = 2² × 733 × 40,031 = 117,370,892

composite factor = 2⁴ × 3 × 71 × 40,031 = 136,425,648

composite factor = 5 × 733 × 40,031 = 146,713,615

composite factor = 2² × 3 × 5 × 71 × 40,031 = 170,532,060

composite factor = 2 × 3 × 733 × 40,031 = 176,056,338

composite factor = 2⁴ × 5 × 71 × 40,031 = 227,376,080

composite factor = 2³ × 733 × 40,031 = 234,741,784

composite factor = 2⁵ × 3 × 71 × 40,031 = 272,851,296

composite factor = 2 × 5 × 733 × 40,031 = 293,427,230

composite factor = 2³ × 3 × 5 × 71 × 40,031 = 341,064,120

composite factor = 2² × 3 × 733 × 40,031 = 352,112,676

composite factor = 3 × 5 × 733 × 40,031 = 440,140,845

composite factor = 2⁵ × 5 × 71 × 40,031 = 454,752,160

composite factor = 2⁴ × 733 × 40,031 = 469,483,568

composite factor = 2² × 5 × 733 × 40,031 = 586,854,460

composite factor = 2⁴ × 3 × 5 × 71 × 40,031 = 682,128,240

composite factor = 2³ × 3 × 733 × 40,031 = 704,225,352

composite factor = 2 × 3 × 5 × 733 × 40,031 = 880,281,690

composite factor = 2⁵ × 733 × 40,031 = 938,967,136

composite factor = 2³ × 5 × 733 × 40,031 = 1,173,708,920

composite factor = 2⁵ × 3 × 5 × 71 × 40,031 = 1,364,256,480

composite factor = 2⁴ × 3 × 733 × 40,031 = 1,408,450,704

composite factor = 2² × 3 × 5 × 733 × 40,031 = 1,760,563,380

composite factor = 71 × 733 × 40,031 = 2,083,333,333

composite factor = 2⁴ × 5 × 733 × 40,031 = 2,347,417,840

composite factor = 2⁵ × 3 × 733 × 40,031 = 2,816,901,408

composite factor = 2³ × 3 × 5 × 733 × 40,031 = 3,521,126,760

composite factor = 2 × 71 × 733 × 40,031 = 4,166,666,666

composite factor = 2⁵ × 5 × 733 × 40,031 = 4,694,835,680

composite factor = 3 × 71 × 733 × 40,031 = 6,249,999,999

composite factor = 2⁴ × 3 × 5 × 733 × 40,031 = 7,042,253,520

composite factor = 2² × 71 × 733 × 40,031 = 8,333,333,332

composite factor = 5 × 71 × 733 × 40,031 = 10,416,666,665

composite factor = 2 × 3 × 71 × 733 × 40,031 = 12,499,999,998

composite factor = 2⁵ × 3 × 5 × 733 × 40,031 = 14,084,507,040

composite factor = 2³ × 71 × 733 × 40,031 = 16,666,666,664

composite factor = 2 × 5 × 71 × 733 × 40,031 = 20,833,333,330

composite factor = 2² × 3 × 71 × 733 × 40,031 = 24,999,999,996

composite factor = 3 × 5 × 71 × 733 × 40,031 = 31,249,999,995

composite factor = 2⁴ × 71 × 733 × 40,031 = 33,333,333,328

composite factor = 2² × 5 × 71 × 733 × 40,031 = 41,666,666,660

composite factor = 2³ × 3 × 71 × 733 × 40,031 = 49,999,999,992

composite factor = 2 × 3 × 5 × 71 × 733 × 40,031 = 62,499,999,990

composite factor = 2⁵ × 71 × 733 × 40,031 = 66,666,666,656

composite factor = 2³ × 5 × 71 × 733 × 40,031 = 83,333,333,320

composite factor = 2⁴ × 3 × 71 × 733 × 40,031 = 99,999,999,984

composite factor = 2² × 3 × 5 × 71 × 733 × 40,031 = 124,999,999,980

composite factor = 2⁴ × 5 × 71 × 733 × 40,031 = 166,666,666,640

composite factor = 2⁵ × 3 × 71 × 733 × 40,031 = 199,999,999,968

composite factor = 2³ × 3 × 5 × 71 × 733 × 40,031 = 249,999,999,960

composite factor = 2⁵ × 5 × 71 × 733 × 40,031 = 333,333,333,280

composite factor = 2⁴ × 3 × 5 × 71 × 733 × 40,031 = 499,999,999,920

composite factor = 2⁵ × 3 × 5 × 71 × 733 × 40,031 = 999,999,999,840

192 factors (divisors)

What times what is 999,999,999,840?
What number multiplied by what number equals 999,999,999,840?

All the combinations of any two natural numbers whose product equals 999,999,999,840.

1 × 999,999,999,840 = 999,999,999,840

2 × 499,999,999,920 = 999,999,999,840

3 × 333,333,333,280 = 999,999,999,840

4 × 249,999,999,960 = 999,999,999,840

5 × 199,999,999,968 = 999,999,999,840

6 × 166,666,666,640 = 999,999,999,840

8 × 124,999,999,980 = 999,999,999,840

10 × 99,999,999,984 = 999,999,999,840

12 × 83,333,333,320 = 999,999,999,840

15 × 66,666,666,656 = 999,999,999,840

16 × 62,499,999,990 = 999,999,999,840

20 × 49,999,999,992 = 999,999,999,840

24 × 41,666,666,660 = 999,999,999,840

30 × 33,333,333,328 = 999,999,999,840

32 × 31,249,999,995 = 999,999,999,840

40 × 24,999,999,996 = 999,999,999,840

48 × 20,833,333,330 = 999,999,999,840

60 × 16,666,666,664 = 999,999,999,840

71 × 14,084,507,040 = 999,999,999,840

80 × 12,499,999,998 = 999,999,999,840

96 × 10,416,666,665 = 999,999,999,840

120 × 8,333,333,332 = 999,999,999,840

142 × 7,042,253,520 = 999,999,999,840

160 × 6,249,999,999 = 999,999,999,840

213 × 4,694,835,680 = 999,999,999,840

240 × 4,166,666,666 = 999,999,999,840

284 × 3,521,126,760 = 999,999,999,840

355 × 2,816,901,408 = 999,999,999,840

426 × 2,347,417,840 = 999,999,999,840

480 × 2,083,333,333 = 999,999,999,840

568 × 1,760,563,380 = 999,999,999,840

710 × 1,408,450,704 = 999,999,999,840

733 × 1,364,256,480 = 999,999,999,840

852 × 1,173,708,920 = 999,999,999,840

1,065 × 938,967,136 = 999,999,999,840

1,136 × 880,281,690 = 999,999,999,840

1,420 × 704,225,352 = 999,999,999,840

1,466 × 682,128,240 = 999,999,999,840

1,704 × 586,854,460 = 999,999,999,840

2,130 × 469,483,568 = 999,999,999,840

2,199 × 454,752,160 = 999,999,999,840

2,272 × 440,140,845 = 999,999,999,840

2,840 × 352,112,676 = 999,999,999,840

2,932 × 341,064,120 = 999,999,999,840

3,408 × 293,427,230 = 999,999,999,840

3,665 × 272,851,296 = 999,999,999,840

4,260 × 234,741,784 = 999,999,999,840

4,398 × 227,376,080 = 999,999,999,840

5,680 × 176,056,338 = 999,999,999,840

5,864 × 170,532,060 = 999,999,999,840

6,816 × 146,713,615 = 999,999,999,840

7,330 × 136,425,648 = 999,999,999,840

8,520 × 117,370,892 = 999,999,999,840

8,796 × 113,688,040 = 999,999,999,840

10,995 × 90,950,432 = 999,999,999,840

11,360 × 88,028,169 = 999,999,999,840

11,728 × 85,266,030 = 999,999,999,840

14,660 × 68,212,824 = 999,999,999,840

17,040 × 58,685,446 = 999,999,999,840

17,592 × 56,844,020 = 999,999,999,840

21,990 × 45,475,216 = 999,999,999,840

23,456 × 42,633,015 = 999,999,999,840

29,320 × 34,106,412 = 999,999,999,840

34,080 × 29,342,723 = 999,999,999,840

35,184 × 28,422,010 = 999,999,999,840

40,031 × 24,980,640 = 999,999,999,840

43,980 × 22,737,608 = 999,999,999,840

52,043 × 19,214,880 = 999,999,999,840

58,640 × 17,053,206 = 999,999,999,840

70,368 × 14,211,005 = 999,999,999,840

80,062 × 12,490,320 = 999,999,999,840

87,960 × 11,368,804 = 999,999,999,840

104,086 × 9,607,440 = 999,999,999,840

117,280 × 8,526,603 = 999,999,999,840

120,093 × 8,326,880 = 999,999,999,840

156,129 × 6,404,960 = 999,999,999,840

160,124 × 6,245,160 = 999,999,999,840

175,920 × 5,684,402 = 999,999,999,840

200,155 × 4,996,128 = 999,999,999,840

208,172 × 4,803,720 = 999,999,999,840

240,186 × 4,163,440 = 999,999,999,840

260,215 × 3,842,976 = 999,999,999,840

312,258 × 3,202,480 = 999,999,999,840

320,248 × 3,122,580 = 999,999,999,840

351,840 × 2,842,201 = 999,999,999,840

400,310 × 2,498,064 = 999,999,999,840

416,344 × 2,401,860 = 999,999,999,840

480,372 × 2,081,720 = 999,999,999,840

520,430 × 1,921,488 = 999,999,999,840

600,465 × 1,665,376 = 999,999,999,840

624,516 × 1,601,240 = 999,999,999,840

640,496 × 1,561,290 = 999,999,999,840

780,645 × 1,280,992 = 999,999,999,840

800,620 × 1,249,032 = 999,999,999,840

832,688 × 1,200,930 = 999,999,999,840

960,744 × 1,040,860 = 999,999,999,840

96 unique multiplications

The final answer:
(scroll down)

999,999,999,840 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 15; 16; 20; 24; 30; 32; 40; 48; 60; 71; 80; 96; 120; 142; 160; 213; 240; 284; 355; 426; 480; 568; 710; 733; 852; 1,065; 1,136; 1,420; 1,466; 1,704; 2,130; 2,199; 2,272; 2,840; 2,932; 3,408; 3,665; 4,260; 4,398; 5,680; 5,864; 6,816; 7,330; 8,520; 8,796; 10,995; 11,360; 11,728; 14,660; 17,040; 17,592; 21,990; 23,456; 29,320; 34,080; 35,184; 40,031; 43,980; 52,043; 58,640; 70,368; 80,062; 87,960; 104,086; 117,280; 120,093; 156,129; 160,124; 175,920; 200,155; 208,172; 240,186; 260,215; 312,258; 320,248; 351,840; 400,310; 416,344; 480,372; 520,430; 600,465; 624,516; 640,496; 780,645; 800,620; 832,688; 960,744; 1,040,860; 1,200,930; 1,249,032; 1,280,992; 1,561,290; 1,601,240; 1,665,376; 1,921,488; 2,081,720; 2,401,860; 2,498,064; 2,842,201; 3,122,580; 3,202,480; 3,842,976; 4,163,440; 4,803,720; 4,996,128; 5,684,402; 6,245,160; 6,404,960; 8,326,880; 8,526,603; 9,607,440; 11,368,804; 12,490,320; 14,211,005; 17,053,206; 19,214,880; 22,737,608; 24,980,640; 28,422,010; 29,342,723; 34,106,412; 42,633,015; 45,475,216; 56,844,020; 58,685,446; 68,212,824; 85,266,030; 88,028,169; 90,950,432; 113,688,040; 117,370,892; 136,425,648; 146,713,615; 170,532,060; 176,056,338; 227,376,080; 234,741,784; 272,851,296; 293,427,230; 341,064,120; 352,112,676; 440,140,845; 454,752,160; 469,483,568; 586,854,460; 682,128,240; 704,225,352; 880,281,690; 938,967,136; 1,173,708,920; 1,364,256,480; 1,408,450,704; 1,760,563,380; 2,083,333,333; 2,347,417,840; 2,816,901,408; 3,521,126,760; 4,166,666,666; 4,694,835,680; 6,249,999,999; 7,042,253,520; 8,333,333,332; 10,416,666,665; 12,499,999,998; 14,084,507,040; 16,666,666,664; 20,833,333,330; 24,999,999,996; 31,249,999,995; 33,333,333,328; 41,666,666,660; 49,999,999,992; 62,499,999,990; 66,666,666,656; 83,333,333,320; 99,999,999,984; 124,999,999,980; 166,666,666,640; 199,999,999,968; 249,999,999,960; 333,333,333,280; 499,999,999,920 and 999,999,999,840
out of which 6 prime factors: 2; 3; 5; 71; 733 and 40,031.
Numbers other than 1 that are not prime factors are composite factors (divisors).
999,999,999,840 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.
Then multiply the prime factors and their exponents, if any, in all their different combinations.

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Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
Hint: 2³ = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 2³ is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.

For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
12 = 2 × 2 × 3 = 2² × 3
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5
120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".

For example, 12 is the common factor of 48 and 360.
The remainder is zero when dividing either 48 or 360 by 12.
Here there are the prime factorizations of the three numbers, 12, 48 and 360:
12 = 2² × 3
48 = 2⁴ × 3
360 = 2³ × 3² × 5
Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...

GCF, GCD (1,260; 3,024; 5,544) = ?
1,260 = 2² × 3²
3,024 = 2⁴ × 3² × 7
5,544 = 2³ × 3² × 7 × 11
The common prime factors are:
2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
GCF, GCD (1,260; 3,024; 5,544) = 2² × 3² = 252

Coprime numbers:
If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

Factors of the GCF
If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".