Factors of 990,360. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 990,360. Connection with the prime factorization of the number

To find all the divisors of the number 990,360:

  • 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 990,360:

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


990,360 = 23 × 33 × 5 × 7 × 131
990,360 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 = am × bk × cz
    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 = (3 + 1) × (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 4 × 4 × 2 × 2 × 2 = 128

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

2. Multiply the prime factors of the number 990,360

  • 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
prime factor = 7
composite factor = 23 = 8
composite factor = 32 = 9
composite factor = 2 × 5 = 10
composite factor = 22 × 3 = 12
composite factor = 2 × 7 = 14
composite factor = 3 × 5 = 15
composite factor = 2 × 32 = 18
composite factor = 22 × 5 = 20
composite factor = 3 × 7 = 21
composite factor = 23 × 3 = 24
composite factor = 33 = 27
composite factor = 22 × 7 = 28
composite factor = 2 × 3 × 5 = 30
composite factor = 5 × 7 = 35
composite factor = 22 × 32 = 36
composite factor = 23 × 5 = 40
composite factor = 2 × 3 × 7 = 42
composite factor = 32 × 5 = 45
composite factor = 2 × 33 = 54
composite factor = 23 × 7 = 56
composite factor = 22 × 3 × 5 = 60
composite factor = 32 × 7 = 63
composite factor = 2 × 5 × 7 = 70
composite factor = 23 × 32 = 72
composite factor = 22 × 3 × 7 = 84
composite factor = 2 × 32 × 5 = 90
composite factor = 3 × 5 × 7 = 105
composite factor = 22 × 33 = 108
composite factor = 23 × 3 × 5 = 120
composite factor = 2 × 32 × 7 = 126
prime factor = 131
composite factor = 33 × 5 = 135
composite factor = 22 × 5 × 7 = 140
composite factor = 23 × 3 × 7 = 168
composite factor = 22 × 32 × 5 = 180
composite factor = 33 × 7 = 189
composite factor = 2 × 3 × 5 × 7 = 210
composite factor = 23 × 33 = 216
composite factor = 22 × 32 × 7 = 252
composite factor = 2 × 131 = 262
composite factor = 2 × 33 × 5 = 270
composite factor = 23 × 5 × 7 = 280
composite factor = 32 × 5 × 7 = 315
composite factor = 23 × 32 × 5 = 360
composite factor = 2 × 33 × 7 = 378
composite factor = 3 × 131 = 393
composite factor = 22 × 3 × 5 × 7 = 420
composite factor = 23 × 32 × 7 = 504
composite factor = 22 × 131 = 524
composite factor = 22 × 33 × 5 = 540
composite factor = 2 × 32 × 5 × 7 = 630
composite factor = 5 × 131 = 655
composite factor = 22 × 33 × 7 = 756
composite factor = 2 × 3 × 131 = 786
composite factor = 23 × 3 × 5 × 7 = 840
composite factor = 7 × 131 = 917
composite factor = 33 × 5 × 7 = 945
This list continues below...

... This list continues from above
composite factor = 23 × 131 = 1,048
composite factor = 23 × 33 × 5 = 1,080
composite factor = 32 × 131 = 1,179
composite factor = 22 × 32 × 5 × 7 = 1,260
composite factor = 2 × 5 × 131 = 1,310
composite factor = 23 × 33 × 7 = 1,512
composite factor = 22 × 3 × 131 = 1,572
composite factor = 2 × 7 × 131 = 1,834
composite factor = 2 × 33 × 5 × 7 = 1,890
composite factor = 3 × 5 × 131 = 1,965
composite factor = 2 × 32 × 131 = 2,358
composite factor = 23 × 32 × 5 × 7 = 2,520
composite factor = 22 × 5 × 131 = 2,620
composite factor = 3 × 7 × 131 = 2,751
composite factor = 23 × 3 × 131 = 3,144
composite factor = 33 × 131 = 3,537
composite factor = 22 × 7 × 131 = 3,668
composite factor = 22 × 33 × 5 × 7 = 3,780
composite factor = 2 × 3 × 5 × 131 = 3,930
composite factor = 5 × 7 × 131 = 4,585
composite factor = 22 × 32 × 131 = 4,716
composite factor = 23 × 5 × 131 = 5,240
composite factor = 2 × 3 × 7 × 131 = 5,502
composite factor = 32 × 5 × 131 = 5,895
composite factor = 2 × 33 × 131 = 7,074
composite factor = 23 × 7 × 131 = 7,336
composite factor = 23 × 33 × 5 × 7 = 7,560
composite factor = 22 × 3 × 5 × 131 = 7,860
composite factor = 32 × 7 × 131 = 8,253
composite factor = 2 × 5 × 7 × 131 = 9,170
composite factor = 23 × 32 × 131 = 9,432
composite factor = 22 × 3 × 7 × 131 = 11,004
composite factor = 2 × 32 × 5 × 131 = 11,790
composite factor = 3 × 5 × 7 × 131 = 13,755
composite factor = 22 × 33 × 131 = 14,148
composite factor = 23 × 3 × 5 × 131 = 15,720
composite factor = 2 × 32 × 7 × 131 = 16,506
composite factor = 33 × 5 × 131 = 17,685
composite factor = 22 × 5 × 7 × 131 = 18,340
composite factor = 23 × 3 × 7 × 131 = 22,008
composite factor = 22 × 32 × 5 × 131 = 23,580
composite factor = 33 × 7 × 131 = 24,759
composite factor = 2 × 3 × 5 × 7 × 131 = 27,510
composite factor = 23 × 33 × 131 = 28,296
composite factor = 22 × 32 × 7 × 131 = 33,012
composite factor = 2 × 33 × 5 × 131 = 35,370
composite factor = 23 × 5 × 7 × 131 = 36,680
composite factor = 32 × 5 × 7 × 131 = 41,265
composite factor = 23 × 32 × 5 × 131 = 47,160
composite factor = 2 × 33 × 7 × 131 = 49,518
composite factor = 22 × 3 × 5 × 7 × 131 = 55,020
composite factor = 23 × 32 × 7 × 131 = 66,024
composite factor = 22 × 33 × 5 × 131 = 70,740
composite factor = 2 × 32 × 5 × 7 × 131 = 82,530
composite factor = 22 × 33 × 7 × 131 = 99,036
composite factor = 23 × 3 × 5 × 7 × 131 = 110,040
composite factor = 33 × 5 × 7 × 131 = 123,795
composite factor = 23 × 33 × 5 × 131 = 141,480
composite factor = 22 × 32 × 5 × 7 × 131 = 165,060
composite factor = 23 × 33 × 7 × 131 = 198,072
composite factor = 2 × 33 × 5 × 7 × 131 = 247,590
composite factor = 23 × 32 × 5 × 7 × 131 = 330,120
composite factor = 22 × 33 × 5 × 7 × 131 = 495,180
composite factor = 23 × 33 × 5 × 7 × 131 = 990,360
128 factors (divisors)

What times what is 990,360?
What number multiplied by what number equals 990,360?

All the combinations of any two natural numbers whose product equals 990,360.

1 × 990,360 = 990,360
2 × 495,180 = 990,360
3 × 330,120 = 990,360
4 × 247,590 = 990,360
5 × 198,072 = 990,360
6 × 165,060 = 990,360
7 × 141,480 = 990,360
8 × 123,795 = 990,360
9 × 110,040 = 990,360
10 × 99,036 = 990,360
12 × 82,530 = 990,360
14 × 70,740 = 990,360
15 × 66,024 = 990,360
18 × 55,020 = 990,360
20 × 49,518 = 990,360
21 × 47,160 = 990,360
24 × 41,265 = 990,360
27 × 36,680 = 990,360
28 × 35,370 = 990,360
30 × 33,012 = 990,360
35 × 28,296 = 990,360
36 × 27,510 = 990,360
40 × 24,759 = 990,360
42 × 23,580 = 990,360
45 × 22,008 = 990,360
54 × 18,340 = 990,360
56 × 17,685 = 990,360
60 × 16,506 = 990,360
63 × 15,720 = 990,360
70 × 14,148 = 990,360
72 × 13,755 = 990,360
84 × 11,790 = 990,360
90 × 11,004 = 990,360
105 × 9,432 = 990,360
108 × 9,170 = 990,360
120 × 8,253 = 990,360
126 × 7,860 = 990,360
131 × 7,560 = 990,360
135 × 7,336 = 990,360
140 × 7,074 = 990,360
168 × 5,895 = 990,360
180 × 5,502 = 990,360
189 × 5,240 = 990,360
210 × 4,716 = 990,360
216 × 4,585 = 990,360
252 × 3,930 = 990,360
262 × 3,780 = 990,360
270 × 3,668 = 990,360
280 × 3,537 = 990,360
315 × 3,144 = 990,360
360 × 2,751 = 990,360
378 × 2,620 = 990,360
393 × 2,520 = 990,360
420 × 2,358 = 990,360
504 × 1,965 = 990,360
524 × 1,890 = 990,360
540 × 1,834 = 990,360
630 × 1,572 = 990,360
655 × 1,512 = 990,360
756 × 1,310 = 990,360
786 × 1,260 = 990,360
840 × 1,179 = 990,360
917 × 1,080 = 990,360
945 × 1,048 = 990,360
64 unique multiplications

The final answer:
(scroll down)


990,360 has 128 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 18; 20; 21; 24; 27; 28; 30; 35; 36; 40; 42; 45; 54; 56; 60; 63; 70; 72; 84; 90; 105; 108; 120; 126; 131; 135; 140; 168; 180; 189; 210; 216; 252; 262; 270; 280; 315; 360; 378; 393; 420; 504; 524; 540; 630; 655; 756; 786; 840; 917; 945; 1,048; 1,080; 1,179; 1,260; 1,310; 1,512; 1,572; 1,834; 1,890; 1,965; 2,358; 2,520; 2,620; 2,751; 3,144; 3,537; 3,668; 3,780; 3,930; 4,585; 4,716; 5,240; 5,502; 5,895; 7,074; 7,336; 7,560; 7,860; 8,253; 9,170; 9,432; 11,004; 11,790; 13,755; 14,148; 15,720; 16,506; 17,685; 18,340; 22,008; 23,580; 24,759; 27,510; 28,296; 33,012; 35,370; 36,680; 41,265; 47,160; 49,518; 55,020; 66,024; 70,740; 82,530; 99,036; 110,040; 123,795; 141,480; 165,060; 198,072; 247,590; 330,120; 495,180 and 990,360
out of which 5 prime factors: 2; 3; 5; 7 and 131.
Numbers other than 1 that are not prime factors are composite factors (divisors).
990,360 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".