Factors of 102,400,000,110. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 102,400,000,110. 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 102,400,000,110:

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 102,400,000,110:

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

102,400,000,110 = 2 × 3² × 5 × 19³ × 31 × 5,351
102,400,000,110 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 = (1 + 1) × (2 + 1) × (1 + 1) × (3 + 1) × (1 + 1) × (1 + 1) = 2 × 3 × 2 × 4 × 2 × 2 = 192

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

2. Multiply the prime factors of the number 102,400,000,110

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

prime factor = 5

composite factor = 2 × 3 = 6

composite factor = 3² = 9

composite factor = 2 × 5 = 10

composite factor = 3 × 5 = 15

composite factor = 2 × 3² = 18

prime factor = 19

composite factor = 2 × 3 × 5 = 30

prime factor = 31

composite factor = 2 × 19 = 38

composite factor = 3² × 5 = 45

composite factor = 3 × 19 = 57

composite factor = 2 × 31 = 62

composite factor = 2 × 3² × 5 = 90

composite factor = 3 × 31 = 93

composite factor = 5 × 19 = 95

composite factor = 2 × 3 × 19 = 114

composite factor = 5 × 31 = 155

composite factor = 3² × 19 = 171

composite factor = 2 × 3 × 31 = 186

composite factor = 2 × 5 × 19 = 190

composite factor = 3² × 31 = 279

composite factor = 3 × 5 × 19 = 285

composite factor = 2 × 5 × 31 = 310

composite factor = 2 × 3² × 19 = 342

composite factor = 19² = 361

composite factor = 3 × 5 × 31 = 465

composite factor = 2 × 3² × 31 = 558

composite factor = 2 × 3 × 5 × 19 = 570

composite factor = 19 × 31 = 589

composite factor = 2 × 19² = 722

composite factor = 3² × 5 × 19 = 855

composite factor = 2 × 3 × 5 × 31 = 930

composite factor = 3 × 19² = 1,083

composite factor = 2 × 19 × 31 = 1,178

composite factor = 3² × 5 × 31 = 1,395

composite factor = 2 × 3² × 5 × 19 = 1,710

composite factor = 3 × 19 × 31 = 1,767

composite factor = 5 × 19² = 1,805

composite factor = 2 × 3 × 19² = 2,166

composite factor = 2 × 3² × 5 × 31 = 2,790

composite factor = 5 × 19 × 31 = 2,945

composite factor = 3² × 19² = 3,249

composite factor = 2 × 3 × 19 × 31 = 3,534

composite factor = 2 × 5 × 19² = 3,610

composite factor = 3² × 19 × 31 = 5,301

prime factor = 5,351

composite factor = 3 × 5 × 19² = 5,415

composite factor = 2 × 5 × 19 × 31 = 5,890

composite factor = 2 × 3² × 19² = 6,498

composite factor = 19³ = 6,859

composite factor = 3 × 5 × 19 × 31 = 8,835

composite factor = 2 × 3² × 19 × 31 = 10,602

composite factor = 2 × 5,351 = 10,702

composite factor = 2 × 3 × 5 × 19² = 10,830

composite factor = 19² × 31 = 11,191

composite factor = 2 × 19³ = 13,718

composite factor = 3 × 5,351 = 16,053

composite factor = 3² × 5 × 19² = 16,245

composite factor = 2 × 3 × 5 × 19 × 31 = 17,670

composite factor = 3 × 19³ = 20,577

composite factor = 2 × 19² × 31 = 22,382

composite factor = 3² × 5 × 19 × 31 = 26,505

composite factor = 5 × 5,351 = 26,755

composite factor = 2 × 3 × 5,351 = 32,106

composite factor = 2 × 3² × 5 × 19² = 32,490

composite factor = 3 × 19² × 31 = 33,573

composite factor = 5 × 19³ = 34,295

composite factor = 2 × 3 × 19³ = 41,154

composite factor = 3² × 5,351 = 48,159

composite factor = 2 × 3² × 5 × 19 × 31 = 53,010

composite factor = 2 × 5 × 5,351 = 53,510

composite factor = 5 × 19² × 31 = 55,955

composite factor = 3² × 19³ = 61,731

composite factor = 2 × 3 × 19² × 31 = 67,146

composite factor = 2 × 5 × 19³ = 68,590

composite factor = 3 × 5 × 5,351 = 80,265

composite factor = 2 × 3² × 5,351 = 96,318

composite factor = 3² × 19² × 31 = 100,719

composite factor = 19 × 5,351 = 101,669

composite factor = 3 × 5 × 19³ = 102,885

composite factor = 2 × 5 × 19² × 31 = 111,910

composite factor = 2 × 3² × 19³ = 123,462

composite factor = 2 × 3 × 5 × 5,351 = 160,530

composite factor = 31 × 5,351 = 165,881

composite factor = 3 × 5 × 19² × 31 = 167,865

composite factor = 2 × 3² × 19² × 31 = 201,438

composite factor = 2 × 19 × 5,351 = 203,338

composite factor = 2 × 3 × 5 × 19³ = 205,770

composite factor = 19³ × 31 = 212,629

composite factor = 3² × 5 × 5,351 = 240,795

composite factor = 3 × 19 × 5,351 = 305,007

composite factor = 3² × 5 × 19³ = 308,655

This list continues below...

... This list continues from above

composite factor = 2 × 31 × 5,351 = 331,762

composite factor = 2 × 3 × 5 × 19² × 31 = 335,730

composite factor = 2 × 19³ × 31 = 425,258

composite factor = 2 × 3² × 5 × 5,351 = 481,590

composite factor = 3 × 31 × 5,351 = 497,643

composite factor = 3² × 5 × 19² × 31 = 503,595

composite factor = 5 × 19 × 5,351 = 508,345

composite factor = 2 × 3 × 19 × 5,351 = 610,014

composite factor = 2 × 3² × 5 × 19³ = 617,310

composite factor = 3 × 19³ × 31 = 637,887

composite factor = 5 × 31 × 5,351 = 829,405

composite factor = 3² × 19 × 5,351 = 915,021

composite factor = 2 × 3 × 31 × 5,351 = 995,286

composite factor = 2 × 3² × 5 × 19² × 31 = 1,007,190

composite factor = 2 × 5 × 19 × 5,351 = 1,016,690

composite factor = 5 × 19³ × 31 = 1,063,145

composite factor = 2 × 3 × 19³ × 31 = 1,275,774

composite factor = 3² × 31 × 5,351 = 1,492,929

composite factor = 3 × 5 × 19 × 5,351 = 1,525,035

composite factor = 2 × 5 × 31 × 5,351 = 1,658,810

composite factor = 2 × 3² × 19 × 5,351 = 1,830,042

composite factor = 3² × 19³ × 31 = 1,913,661

composite factor = 19² × 5,351 = 1,931,711

composite factor = 2 × 5 × 19³ × 31 = 2,126,290

composite factor = 3 × 5 × 31 × 5,351 = 2,488,215

composite factor = 2 × 3² × 31 × 5,351 = 2,985,858

composite factor = 2 × 3 × 5 × 19 × 5,351 = 3,050,070

composite factor = 19 × 31 × 5,351 = 3,151,739

composite factor = 3 × 5 × 19³ × 31 = 3,189,435

composite factor = 2 × 3² × 19³ × 31 = 3,827,322

composite factor = 2 × 19² × 5,351 = 3,863,422

composite factor = 3² × 5 × 19 × 5,351 = 4,575,105

composite factor = 2 × 3 × 5 × 31 × 5,351 = 4,976,430

composite factor = 3 × 19² × 5,351 = 5,795,133

composite factor = 2 × 19 × 31 × 5,351 = 6,303,478

composite factor = 2 × 3 × 5 × 19³ × 31 = 6,378,870

composite factor = 3² × 5 × 31 × 5,351 = 7,464,645

composite factor = 2 × 3² × 5 × 19 × 5,351 = 9,150,210

composite factor = 3 × 19 × 31 × 5,351 = 9,455,217

composite factor = 3² × 5 × 19³ × 31 = 9,568,305

composite factor = 5 × 19² × 5,351 = 9,658,555

composite factor = 2 × 3 × 19² × 5,351 = 11,590,266

composite factor = 2 × 3² × 5 × 31 × 5,351 = 14,929,290

composite factor = 5 × 19 × 31 × 5,351 = 15,758,695

composite factor = 3² × 19² × 5,351 = 17,385,399

composite factor = 2 × 3 × 19 × 31 × 5,351 = 18,910,434

composite factor = 2 × 3² × 5 × 19³ × 31 = 19,136,610

composite factor = 2 × 5 × 19² × 5,351 = 19,317,110

composite factor = 3² × 19 × 31 × 5,351 = 28,365,651

composite factor = 3 × 5 × 19² × 5,351 = 28,975,665

composite factor = 2 × 5 × 19 × 31 × 5,351 = 31,517,390

composite factor = 2 × 3² × 19² × 5,351 = 34,770,798

composite factor = 19³ × 5,351 = 36,702,509

composite factor = 3 × 5 × 19 × 31 × 5,351 = 47,276,085

composite factor = 2 × 3² × 19 × 31 × 5,351 = 56,731,302

composite factor = 2 × 3 × 5 × 19² × 5,351 = 57,951,330

composite factor = 19² × 31 × 5,351 = 59,883,041

composite factor = 2 × 19³ × 5,351 = 73,405,018

composite factor = 3² × 5 × 19² × 5,351 = 86,926,995

composite factor = 2 × 3 × 5 × 19 × 31 × 5,351 = 94,552,170

composite factor = 3 × 19³ × 5,351 = 110,107,527

composite factor = 2 × 19² × 31 × 5,351 = 119,766,082

composite factor = 3² × 5 × 19 × 31 × 5,351 = 141,828,255

composite factor = 2 × 3² × 5 × 19² × 5,351 = 173,853,990

composite factor = 3 × 19² × 31 × 5,351 = 179,649,123

composite factor = 5 × 19³ × 5,351 = 183,512,545

composite factor = 2 × 3 × 19³ × 5,351 = 220,215,054

composite factor = 2 × 3² × 5 × 19 × 31 × 5,351 = 283,656,510

composite factor = 5 × 19² × 31 × 5,351 = 299,415,205

composite factor = 3² × 19³ × 5,351 = 330,322,581

composite factor = 2 × 3 × 19² × 31 × 5,351 = 359,298,246

composite factor = 2 × 5 × 19³ × 5,351 = 367,025,090

composite factor = 3² × 19² × 31 × 5,351 = 538,947,369

composite factor = 3 × 5 × 19³ × 5,351 = 550,537,635

composite factor = 2 × 5 × 19² × 31 × 5,351 = 598,830,410

composite factor = 2 × 3² × 19³ × 5,351 = 660,645,162

composite factor = 3 × 5 × 19² × 31 × 5,351 = 898,245,615

composite factor = 2 × 3² × 19² × 31 × 5,351 = 1,077,894,738

composite factor = 2 × 3 × 5 × 19³ × 5,351 = 1,101,075,270

composite factor = 19³ × 31 × 5,351 = 1,137,777,779

composite factor = 3² × 5 × 19³ × 5,351 = 1,651,612,905

composite factor = 2 × 3 × 5 × 19² × 31 × 5,351 = 1,796,491,230

composite factor = 2 × 19³ × 31 × 5,351 = 2,275,555,558

composite factor = 3² × 5 × 19² × 31 × 5,351 = 2,694,736,845

composite factor = 2 × 3² × 5 × 19³ × 5,351 = 3,303,225,810

composite factor = 3 × 19³ × 31 × 5,351 = 3,413,333,337

composite factor = 2 × 3² × 5 × 19² × 31 × 5,351 = 5,389,473,690

composite factor = 5 × 19³ × 31 × 5,351 = 5,688,888,895

composite factor = 2 × 3 × 19³ × 31 × 5,351 = 6,826,666,674

composite factor = 3² × 19³ × 31 × 5,351 = 10,240,000,011

composite factor = 2 × 5 × 19³ × 31 × 5,351 = 11,377,777,790

composite factor = 3 × 5 × 19³ × 31 × 5,351 = 17,066,666,685

composite factor = 2 × 3² × 19³ × 31 × 5,351 = 20,480,000,022

composite factor = 2 × 3 × 5 × 19³ × 31 × 5,351 = 34,133,333,370

composite factor = 3² × 5 × 19³ × 31 × 5,351 = 51,200,000,055

composite factor = 2 × 3² × 5 × 19³ × 31 × 5,351 = 102,400,000,110

192 factors (divisors)

What times what is 102,400,000,110?
What number multiplied by what number equals 102,400,000,110?

All the combinations of any two natural numbers whose product equals 102,400,000,110.

1 × 102,400,000,110 = 102,400,000,110

2 × 51,200,000,055 = 102,400,000,110

3 × 34,133,333,370 = 102,400,000,110

5 × 20,480,000,022 = 102,400,000,110

6 × 17,066,666,685 = 102,400,000,110

9 × 11,377,777,790 = 102,400,000,110

10 × 10,240,000,011 = 102,400,000,110

15 × 6,826,666,674 = 102,400,000,110

18 × 5,688,888,895 = 102,400,000,110

19 × 5,389,473,690 = 102,400,000,110

30 × 3,413,333,337 = 102,400,000,110

31 × 3,303,225,810 = 102,400,000,110

38 × 2,694,736,845 = 102,400,000,110

45 × 2,275,555,558 = 102,400,000,110

57 × 1,796,491,230 = 102,400,000,110

62 × 1,651,612,905 = 102,400,000,110

90 × 1,137,777,779 = 102,400,000,110

93 × 1,101,075,270 = 102,400,000,110

95 × 1,077,894,738 = 102,400,000,110

114 × 898,245,615 = 102,400,000,110

155 × 660,645,162 = 102,400,000,110

171 × 598,830,410 = 102,400,000,110

186 × 550,537,635 = 102,400,000,110

190 × 538,947,369 = 102,400,000,110

279 × 367,025,090 = 102,400,000,110

285 × 359,298,246 = 102,400,000,110

310 × 330,322,581 = 102,400,000,110

342 × 299,415,205 = 102,400,000,110

361 × 283,656,510 = 102,400,000,110

465 × 220,215,054 = 102,400,000,110

558 × 183,512,545 = 102,400,000,110

570 × 179,649,123 = 102,400,000,110

589 × 173,853,990 = 102,400,000,110

722 × 141,828,255 = 102,400,000,110

855 × 119,766,082 = 102,400,000,110

930 × 110,107,527 = 102,400,000,110

1,083 × 94,552,170 = 102,400,000,110

1,178 × 86,926,995 = 102,400,000,110

1,395 × 73,405,018 = 102,400,000,110

1,710 × 59,883,041 = 102,400,000,110

1,767 × 57,951,330 = 102,400,000,110

1,805 × 56,731,302 = 102,400,000,110

2,166 × 47,276,085 = 102,400,000,110

2,790 × 36,702,509 = 102,400,000,110

2,945 × 34,770,798 = 102,400,000,110

3,249 × 31,517,390 = 102,400,000,110

3,534 × 28,975,665 = 102,400,000,110

3,610 × 28,365,651 = 102,400,000,110

5,301 × 19,317,110 = 102,400,000,110

5,351 × 19,136,610 = 102,400,000,110

5,415 × 18,910,434 = 102,400,000,110

5,890 × 17,385,399 = 102,400,000,110

6,498 × 15,758,695 = 102,400,000,110

6,859 × 14,929,290 = 102,400,000,110

8,835 × 11,590,266 = 102,400,000,110

10,602 × 9,658,555 = 102,400,000,110

10,702 × 9,568,305 = 102,400,000,110

10,830 × 9,455,217 = 102,400,000,110

11,191 × 9,150,210 = 102,400,000,110

13,718 × 7,464,645 = 102,400,000,110

16,053 × 6,378,870 = 102,400,000,110

16,245 × 6,303,478 = 102,400,000,110

17,670 × 5,795,133 = 102,400,000,110

20,577 × 4,976,430 = 102,400,000,110

22,382 × 4,575,105 = 102,400,000,110

26,505 × 3,863,422 = 102,400,000,110

26,755 × 3,827,322 = 102,400,000,110

32,106 × 3,189,435 = 102,400,000,110

32,490 × 3,151,739 = 102,400,000,110

33,573 × 3,050,070 = 102,400,000,110

34,295 × 2,985,858 = 102,400,000,110

41,154 × 2,488,215 = 102,400,000,110

48,159 × 2,126,290 = 102,400,000,110

53,010 × 1,931,711 = 102,400,000,110

53,510 × 1,913,661 = 102,400,000,110

55,955 × 1,830,042 = 102,400,000,110

61,731 × 1,658,810 = 102,400,000,110

67,146 × 1,525,035 = 102,400,000,110

68,590 × 1,492,929 = 102,400,000,110

80,265 × 1,275,774 = 102,400,000,110

96,318 × 1,063,145 = 102,400,000,110

100,719 × 1,016,690 = 102,400,000,110

101,669 × 1,007,190 = 102,400,000,110

102,885 × 995,286 = 102,400,000,110

111,910 × 915,021 = 102,400,000,110

123,462 × 829,405 = 102,400,000,110

160,530 × 637,887 = 102,400,000,110

165,881 × 617,310 = 102,400,000,110

167,865 × 610,014 = 102,400,000,110

201,438 × 508,345 = 102,400,000,110

203,338 × 503,595 = 102,400,000,110

205,770 × 497,643 = 102,400,000,110

212,629 × 481,590 = 102,400,000,110

240,795 × 425,258 = 102,400,000,110

305,007 × 335,730 = 102,400,000,110

308,655 × 331,762 = 102,400,000,110

96 unique multiplications

The final answer:
(scroll down)

102,400,000,110 has 192 factors (divisors):
1; 2; 3; 5; 6; 9; 10; 15; 18; 19; 30; 31; 38; 45; 57; 62; 90; 93; 95; 114; 155; 171; 186; 190; 279; 285; 310; 342; 361; 465; 558; 570; 589; 722; 855; 930; 1,083; 1,178; 1,395; 1,710; 1,767; 1,805; 2,166; 2,790; 2,945; 3,249; 3,534; 3,610; 5,301; 5,351; 5,415; 5,890; 6,498; 6,859; 8,835; 10,602; 10,702; 10,830; 11,191; 13,718; 16,053; 16,245; 17,670; 20,577; 22,382; 26,505; 26,755; 32,106; 32,490; 33,573; 34,295; 41,154; 48,159; 53,010; 53,510; 55,955; 61,731; 67,146; 68,590; 80,265; 96,318; 100,719; 101,669; 102,885; 111,910; 123,462; 160,530; 165,881; 167,865; 201,438; 203,338; 205,770; 212,629; 240,795; 305,007; 308,655; 331,762; 335,730; 425,258; 481,590; 497,643; 503,595; 508,345; 610,014; 617,310; 637,887; 829,405; 915,021; 995,286; 1,007,190; 1,016,690; 1,063,145; 1,275,774; 1,492,929; 1,525,035; 1,658,810; 1,830,042; 1,913,661; 1,931,711; 2,126,290; 2,488,215; 2,985,858; 3,050,070; 3,151,739; 3,189,435; 3,827,322; 3,863,422; 4,575,105; 4,976,430; 5,795,133; 6,303,478; 6,378,870; 7,464,645; 9,150,210; 9,455,217; 9,568,305; 9,658,555; 11,590,266; 14,929,290; 15,758,695; 17,385,399; 18,910,434; 19,136,610; 19,317,110; 28,365,651; 28,975,665; 31,517,390; 34,770,798; 36,702,509; 47,276,085; 56,731,302; 57,951,330; 59,883,041; 73,405,018; 86,926,995; 94,552,170; 110,107,527; 119,766,082; 141,828,255; 173,853,990; 179,649,123; 183,512,545; 220,215,054; 283,656,510; 299,415,205; 330,322,581; 359,298,246; 367,025,090; 538,947,369; 550,537,635; 598,830,410; 660,645,162; 898,245,615; 1,077,894,738; 1,101,075,270; 1,137,777,779; 1,651,612,905; 1,796,491,230; 2,275,555,558; 2,694,736,845; 3,303,225,810; 3,413,333,337; 5,389,473,690; 5,688,888,895; 6,826,666,674; 10,240,000,011; 11,377,777,790; 17,066,666,685; 20,480,000,022; 34,133,333,370; 51,200,000,055 and 102,400,000,110
out of which 6 prime factors: 2; 3; 5; 19; 31 and 5,351.
Numbers other than 1 that are not prime factors are composite factors (divisors).
102,400,000,110 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".