Factors of 972,720. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 972,720. Connection with the prime factorization of the number

To find all the divisors of the number 972,720:

  • 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 972,720:

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


972,720 = 24 × 32 × 5 × 7 × 193
972,720 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 = (4 + 1) × (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 5 × 3 × 2 × 2 × 2 = 120

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

2. Multiply the prime factors of the number 972,720

  • 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 = 24 = 16
composite factor = 2 × 32 = 18
composite factor = 22 × 5 = 20
composite factor = 3 × 7 = 21
composite factor = 23 × 3 = 24
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 = 24 × 3 = 48
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 = 24 × 5 = 80
composite factor = 22 × 3 × 7 = 84
composite factor = 2 × 32 × 5 = 90
composite factor = 3 × 5 × 7 = 105
composite factor = 24 × 7 = 112
composite factor = 23 × 3 × 5 = 120
composite factor = 2 × 32 × 7 = 126
composite factor = 22 × 5 × 7 = 140
composite factor = 24 × 32 = 144
composite factor = 23 × 3 × 7 = 168
composite factor = 22 × 32 × 5 = 180
prime factor = 193
composite factor = 2 × 3 × 5 × 7 = 210
composite factor = 24 × 3 × 5 = 240
composite factor = 22 × 32 × 7 = 252
composite factor = 23 × 5 × 7 = 280
composite factor = 32 × 5 × 7 = 315
composite factor = 24 × 3 × 7 = 336
composite factor = 23 × 32 × 5 = 360
composite factor = 2 × 193 = 386
composite factor = 22 × 3 × 5 × 7 = 420
composite factor = 23 × 32 × 7 = 504
composite factor = 24 × 5 × 7 = 560
composite factor = 3 × 193 = 579
composite factor = 2 × 32 × 5 × 7 = 630
composite factor = 24 × 32 × 5 = 720
composite factor = 22 × 193 = 772
composite factor = 23 × 3 × 5 × 7 = 840
composite factor = 5 × 193 = 965
This list continues below...

... This list continues from above
composite factor = 24 × 32 × 7 = 1,008
composite factor = 2 × 3 × 193 = 1,158
composite factor = 22 × 32 × 5 × 7 = 1,260
composite factor = 7 × 193 = 1,351
composite factor = 23 × 193 = 1,544
composite factor = 24 × 3 × 5 × 7 = 1,680
composite factor = 32 × 193 = 1,737
composite factor = 2 × 5 × 193 = 1,930
composite factor = 22 × 3 × 193 = 2,316
composite factor = 23 × 32 × 5 × 7 = 2,520
composite factor = 2 × 7 × 193 = 2,702
composite factor = 3 × 5 × 193 = 2,895
composite factor = 24 × 193 = 3,088
composite factor = 2 × 32 × 193 = 3,474
composite factor = 22 × 5 × 193 = 3,860
composite factor = 3 × 7 × 193 = 4,053
composite factor = 23 × 3 × 193 = 4,632
composite factor = 24 × 32 × 5 × 7 = 5,040
composite factor = 22 × 7 × 193 = 5,404
composite factor = 2 × 3 × 5 × 193 = 5,790
composite factor = 5 × 7 × 193 = 6,755
composite factor = 22 × 32 × 193 = 6,948
composite factor = 23 × 5 × 193 = 7,720
composite factor = 2 × 3 × 7 × 193 = 8,106
composite factor = 32 × 5 × 193 = 8,685
composite factor = 24 × 3 × 193 = 9,264
composite factor = 23 × 7 × 193 = 10,808
composite factor = 22 × 3 × 5 × 193 = 11,580
composite factor = 32 × 7 × 193 = 12,159
composite factor = 2 × 5 × 7 × 193 = 13,510
composite factor = 23 × 32 × 193 = 13,896
composite factor = 24 × 5 × 193 = 15,440
composite factor = 22 × 3 × 7 × 193 = 16,212
composite factor = 2 × 32 × 5 × 193 = 17,370
composite factor = 3 × 5 × 7 × 193 = 20,265
composite factor = 24 × 7 × 193 = 21,616
composite factor = 23 × 3 × 5 × 193 = 23,160
composite factor = 2 × 32 × 7 × 193 = 24,318
composite factor = 22 × 5 × 7 × 193 = 27,020
composite factor = 24 × 32 × 193 = 27,792
composite factor = 23 × 3 × 7 × 193 = 32,424
composite factor = 22 × 32 × 5 × 193 = 34,740
composite factor = 2 × 3 × 5 × 7 × 193 = 40,530
composite factor = 24 × 3 × 5 × 193 = 46,320
composite factor = 22 × 32 × 7 × 193 = 48,636
composite factor = 23 × 5 × 7 × 193 = 54,040
composite factor = 32 × 5 × 7 × 193 = 60,795
composite factor = 24 × 3 × 7 × 193 = 64,848
composite factor = 23 × 32 × 5 × 193 = 69,480
composite factor = 22 × 3 × 5 × 7 × 193 = 81,060
composite factor = 23 × 32 × 7 × 193 = 97,272
composite factor = 24 × 5 × 7 × 193 = 108,080
composite factor = 2 × 32 × 5 × 7 × 193 = 121,590
composite factor = 24 × 32 × 5 × 193 = 138,960
composite factor = 23 × 3 × 5 × 7 × 193 = 162,120
composite factor = 24 × 32 × 7 × 193 = 194,544
composite factor = 22 × 32 × 5 × 7 × 193 = 243,180
composite factor = 24 × 3 × 5 × 7 × 193 = 324,240
composite factor = 23 × 32 × 5 × 7 × 193 = 486,360
composite factor = 24 × 32 × 5 × 7 × 193 = 972,720
120 factors (divisors)

What times what is 972,720?
What number multiplied by what number equals 972,720?

All the combinations of any two natural numbers whose product equals 972,720.

1 × 972,720 = 972,720
2 × 486,360 = 972,720
3 × 324,240 = 972,720
4 × 243,180 = 972,720
5 × 194,544 = 972,720
6 × 162,120 = 972,720
7 × 138,960 = 972,720
8 × 121,590 = 972,720
9 × 108,080 = 972,720
10 × 97,272 = 972,720
12 × 81,060 = 972,720
14 × 69,480 = 972,720
15 × 64,848 = 972,720
16 × 60,795 = 972,720
18 × 54,040 = 972,720
20 × 48,636 = 972,720
21 × 46,320 = 972,720
24 × 40,530 = 972,720
28 × 34,740 = 972,720
30 × 32,424 = 972,720
35 × 27,792 = 972,720
36 × 27,020 = 972,720
40 × 24,318 = 972,720
42 × 23,160 = 972,720
45 × 21,616 = 972,720
48 × 20,265 = 972,720
56 × 17,370 = 972,720
60 × 16,212 = 972,720
63 × 15,440 = 972,720
70 × 13,896 = 972,720
72 × 13,510 = 972,720
80 × 12,159 = 972,720
84 × 11,580 = 972,720
90 × 10,808 = 972,720
105 × 9,264 = 972,720
112 × 8,685 = 972,720
120 × 8,106 = 972,720
126 × 7,720 = 972,720
140 × 6,948 = 972,720
144 × 6,755 = 972,720
168 × 5,790 = 972,720
180 × 5,404 = 972,720
193 × 5,040 = 972,720
210 × 4,632 = 972,720
240 × 4,053 = 972,720
252 × 3,860 = 972,720
280 × 3,474 = 972,720
315 × 3,088 = 972,720
336 × 2,895 = 972,720
360 × 2,702 = 972,720
386 × 2,520 = 972,720
420 × 2,316 = 972,720
504 × 1,930 = 972,720
560 × 1,737 = 972,720
579 × 1,680 = 972,720
630 × 1,544 = 972,720
720 × 1,351 = 972,720
772 × 1,260 = 972,720
840 × 1,158 = 972,720
965 × 1,008 = 972,720
60 unique multiplications

The final answer:
(scroll down)


972,720 has 120 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 28; 30; 35; 36; 40; 42; 45; 48; 56; 60; 63; 70; 72; 80; 84; 90; 105; 112; 120; 126; 140; 144; 168; 180; 193; 210; 240; 252; 280; 315; 336; 360; 386; 420; 504; 560; 579; 630; 720; 772; 840; 965; 1,008; 1,158; 1,260; 1,351; 1,544; 1,680; 1,737; 1,930; 2,316; 2,520; 2,702; 2,895; 3,088; 3,474; 3,860; 4,053; 4,632; 5,040; 5,404; 5,790; 6,755; 6,948; 7,720; 8,106; 8,685; 9,264; 10,808; 11,580; 12,159; 13,510; 13,896; 15,440; 16,212; 17,370; 20,265; 21,616; 23,160; 24,318; 27,020; 27,792; 32,424; 34,740; 40,530; 46,320; 48,636; 54,040; 60,795; 64,848; 69,480; 81,060; 97,272; 108,080; 121,590; 138,960; 162,120; 194,544; 243,180; 324,240; 486,360 and 972,720
out of which 5 prime factors: 2; 3; 5; 7 and 193.
Numbers other than 1 that are not prime factors are composite factors (divisors).
972,720 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".