Factors of 90,720. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 90,720. Connection with the prime factorization of the number

To find all the divisors of the number 90,720:

  • 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 90,720:

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


90,720 = 25 × 34 × 5 × 7
90,720 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 = (5 + 1) × (4 + 1) × (1 + 1) × (1 + 1) = 6 × 5 × 2 × 2 = 120

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

2. Multiply the prime factors of the number 90,720

  • 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 = 33 = 27
composite factor = 22 × 7 = 28
composite factor = 2 × 3 × 5 = 30
composite factor = 25 = 32
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 = 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 = 24 × 5 = 80
composite factor = 34 = 81
composite factor = 22 × 3 × 7 = 84
composite factor = 2 × 32 × 5 = 90
composite factor = 25 × 3 = 96
composite factor = 3 × 5 × 7 = 105
composite factor = 22 × 33 = 108
composite factor = 24 × 7 = 112
composite factor = 23 × 3 × 5 = 120
composite factor = 2 × 32 × 7 = 126
composite factor = 33 × 5 = 135
composite factor = 22 × 5 × 7 = 140
composite factor = 24 × 32 = 144
composite factor = 25 × 5 = 160
composite factor = 2 × 34 = 162
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 = 25 × 7 = 224
composite factor = 24 × 3 × 5 = 240
composite factor = 22 × 32 × 7 = 252
composite factor = 2 × 33 × 5 = 270
composite factor = 23 × 5 × 7 = 280
composite factor = 25 × 32 = 288
This list continues below...

... This list continues from above
composite factor = 32 × 5 × 7 = 315
composite factor = 22 × 34 = 324
composite factor = 24 × 3 × 7 = 336
composite factor = 23 × 32 × 5 = 360
composite factor = 2 × 33 × 7 = 378
composite factor = 34 × 5 = 405
composite factor = 22 × 3 × 5 × 7 = 420
composite factor = 24 × 33 = 432
composite factor = 25 × 3 × 5 = 480
composite factor = 23 × 32 × 7 = 504
composite factor = 22 × 33 × 5 = 540
composite factor = 24 × 5 × 7 = 560
composite factor = 34 × 7 = 567
composite factor = 2 × 32 × 5 × 7 = 630
composite factor = 23 × 34 = 648
composite factor = 25 × 3 × 7 = 672
composite factor = 24 × 32 × 5 = 720
composite factor = 22 × 33 × 7 = 756
composite factor = 2 × 34 × 5 = 810
composite factor = 23 × 3 × 5 × 7 = 840
composite factor = 25 × 33 = 864
composite factor = 33 × 5 × 7 = 945
composite factor = 24 × 32 × 7 = 1,008
composite factor = 23 × 33 × 5 = 1,080
composite factor = 25 × 5 × 7 = 1,120
composite factor = 2 × 34 × 7 = 1,134
composite factor = 22 × 32 × 5 × 7 = 1,260
composite factor = 24 × 34 = 1,296
composite factor = 25 × 32 × 5 = 1,440
composite factor = 23 × 33 × 7 = 1,512
composite factor = 22 × 34 × 5 = 1,620
composite factor = 24 × 3 × 5 × 7 = 1,680
composite factor = 2 × 33 × 5 × 7 = 1,890
composite factor = 25 × 32 × 7 = 2,016
composite factor = 24 × 33 × 5 = 2,160
composite factor = 22 × 34 × 7 = 2,268
composite factor = 23 × 32 × 5 × 7 = 2,520
composite factor = 25 × 34 = 2,592
composite factor = 34 × 5 × 7 = 2,835
composite factor = 24 × 33 × 7 = 3,024
composite factor = 23 × 34 × 5 = 3,240
composite factor = 25 × 3 × 5 × 7 = 3,360
composite factor = 22 × 33 × 5 × 7 = 3,780
composite factor = 25 × 33 × 5 = 4,320
composite factor = 23 × 34 × 7 = 4,536
composite factor = 24 × 32 × 5 × 7 = 5,040
composite factor = 2 × 34 × 5 × 7 = 5,670
composite factor = 25 × 33 × 7 = 6,048
composite factor = 24 × 34 × 5 = 6,480
composite factor = 23 × 33 × 5 × 7 = 7,560
composite factor = 24 × 34 × 7 = 9,072
composite factor = 25 × 32 × 5 × 7 = 10,080
composite factor = 22 × 34 × 5 × 7 = 11,340
composite factor = 25 × 34 × 5 = 12,960
composite factor = 24 × 33 × 5 × 7 = 15,120
composite factor = 25 × 34 × 7 = 18,144
composite factor = 23 × 34 × 5 × 7 = 22,680
composite factor = 25 × 33 × 5 × 7 = 30,240
composite factor = 24 × 34 × 5 × 7 = 45,360
composite factor = 25 × 34 × 5 × 7 = 90,720
120 factors (divisors)

What times what is 90,720?
What number multiplied by what number equals 90,720?

All the combinations of any two natural numbers whose product equals 90,720.

1 × 90,720 = 90,720
2 × 45,360 = 90,720
3 × 30,240 = 90,720
4 × 22,680 = 90,720
5 × 18,144 = 90,720
6 × 15,120 = 90,720
7 × 12,960 = 90,720
8 × 11,340 = 90,720
9 × 10,080 = 90,720
10 × 9,072 = 90,720
12 × 7,560 = 90,720
14 × 6,480 = 90,720
15 × 6,048 = 90,720
16 × 5,670 = 90,720
18 × 5,040 = 90,720
20 × 4,536 = 90,720
21 × 4,320 = 90,720
24 × 3,780 = 90,720
27 × 3,360 = 90,720
28 × 3,240 = 90,720
30 × 3,024 = 90,720
32 × 2,835 = 90,720
35 × 2,592 = 90,720
36 × 2,520 = 90,720
40 × 2,268 = 90,720
42 × 2,160 = 90,720
45 × 2,016 = 90,720
48 × 1,890 = 90,720
54 × 1,680 = 90,720
56 × 1,620 = 90,720
60 × 1,512 = 90,720
63 × 1,440 = 90,720
70 × 1,296 = 90,720
72 × 1,260 = 90,720
80 × 1,134 = 90,720
81 × 1,120 = 90,720
84 × 1,080 = 90,720
90 × 1,008 = 90,720
96 × 945 = 90,720
105 × 864 = 90,720
108 × 840 = 90,720
112 × 810 = 90,720
120 × 756 = 90,720
126 × 720 = 90,720
135 × 672 = 90,720
140 × 648 = 90,720
144 × 630 = 90,720
160 × 567 = 90,720
162 × 560 = 90,720
168 × 540 = 90,720
180 × 504 = 90,720
189 × 480 = 90,720
210 × 432 = 90,720
216 × 420 = 90,720
224 × 405 = 90,720
240 × 378 = 90,720
252 × 360 = 90,720
270 × 336 = 90,720
280 × 324 = 90,720
288 × 315 = 90,720
60 unique multiplications

The final answer:
(scroll down)


90,720 has 120 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 27; 28; 30; 32; 35; 36; 40; 42; 45; 48; 54; 56; 60; 63; 70; 72; 80; 81; 84; 90; 96; 105; 108; 112; 120; 126; 135; 140; 144; 160; 162; 168; 180; 189; 210; 216; 224; 240; 252; 270; 280; 288; 315; 324; 336; 360; 378; 405; 420; 432; 480; 504; 540; 560; 567; 630; 648; 672; 720; 756; 810; 840; 864; 945; 1,008; 1,080; 1,120; 1,134; 1,260; 1,296; 1,440; 1,512; 1,620; 1,680; 1,890; 2,016; 2,160; 2,268; 2,520; 2,592; 2,835; 3,024; 3,240; 3,360; 3,780; 4,320; 4,536; 5,040; 5,670; 6,048; 6,480; 7,560; 9,072; 10,080; 11,340; 12,960; 15,120; 18,144; 22,680; 30,240; 45,360 and 90,720
out of which 4 prime factors: 2; 3; 5 and 7.
Numbers other than 1 that are not prime factors are composite factors (divisors).
90,720 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".