Factors of 360,000,000. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 360,000,000. Connection with the prime factorization of the number

1. Carry out the prime factorization of the number 360,000,000:

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


360,000,000 = 29 × 32 × 57
360,000,000 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?

  • 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 = (9 + 1) × (2 + 1) × (7 + 1) = 10 × 3 × 8 = 240

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

2. Multiply the prime factors of the number 360,000,000

  • 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
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
23 × 3 = 24
52 = 25
2 × 3 × 5 = 30
25 = 32
22 × 32 = 36
23 × 5 = 40
32 × 5 = 45
24 × 3 = 48
2 × 52 = 50
22 × 3 × 5 = 60
26 = 64
23 × 32 = 72
3 × 52 = 75
24 × 5 = 80
2 × 32 × 5 = 90
25 × 3 = 96
22 × 52 = 100
23 × 3 × 5 = 120
53 = 125
27 = 128
24 × 32 = 144
2 × 3 × 52 = 150
25 × 5 = 160
22 × 32 × 5 = 180
26 × 3 = 192
23 × 52 = 200
32 × 52 = 225
24 × 3 × 5 = 240
2 × 53 = 250
28 = 256
25 × 32 = 288
22 × 3 × 52 = 300
26 × 5 = 320
23 × 32 × 5 = 360
3 × 53 = 375
27 × 3 = 384
24 × 52 = 400
2 × 32 × 52 = 450
25 × 3 × 5 = 480
22 × 53 = 500
29 = 512
26 × 32 = 576
23 × 3 × 52 = 600
54 = 625
27 × 5 = 640
24 × 32 × 5 = 720
2 × 3 × 53 = 750
28 × 3 = 768
25 × 52 = 800
22 × 32 × 52 = 900
26 × 3 × 5 = 960
23 × 53 = 1,000
32 × 53 = 1,125
27 × 32 = 1,152
24 × 3 × 52 = 1,200
2 × 54 = 1,250
28 × 5 = 1,280
25 × 32 × 5 = 1,440
22 × 3 × 53 = 1,500
29 × 3 = 1,536
26 × 52 = 1,600
23 × 32 × 52 = 1,800
3 × 54 = 1,875
27 × 3 × 5 = 1,920
24 × 53 = 2,000
2 × 32 × 53 = 2,250
28 × 32 = 2,304
25 × 3 × 52 = 2,400
22 × 54 = 2,500
29 × 5 = 2,560
26 × 32 × 5 = 2,880
23 × 3 × 53 = 3,000
55 = 3,125
27 × 52 = 3,200
24 × 32 × 52 = 3,600
2 × 3 × 54 = 3,750
28 × 3 × 5 = 3,840
25 × 53 = 4,000
22 × 32 × 53 = 4,500
29 × 32 = 4,608
26 × 3 × 52 = 4,800
23 × 54 = 5,000
32 × 54 = 5,625
27 × 32 × 5 = 5,760
24 × 3 × 53 = 6,000
2 × 55 = 6,250
28 × 52 = 6,400
25 × 32 × 52 = 7,200
22 × 3 × 54 = 7,500
29 × 3 × 5 = 7,680
26 × 53 = 8,000
23 × 32 × 53 = 9,000
3 × 55 = 9,375
27 × 3 × 52 = 9,600
24 × 54 = 10,000
2 × 32 × 54 = 11,250
28 × 32 × 5 = 11,520
25 × 3 × 53 = 12,000
22 × 55 = 12,500
29 × 52 = 12,800
26 × 32 × 52 = 14,400
23 × 3 × 54 = 15,000
56 = 15,625
27 × 53 = 16,000
24 × 32 × 53 = 18,000
2 × 3 × 55 = 18,750
This list continues below...

... This list continues from above
28 × 3 × 52 = 19,200
25 × 54 = 20,000
22 × 32 × 54 = 22,500
29 × 32 × 5 = 23,040
26 × 3 × 53 = 24,000
23 × 55 = 25,000
32 × 55 = 28,125
27 × 32 × 52 = 28,800
24 × 3 × 54 = 30,000
2 × 56 = 31,250
28 × 53 = 32,000
25 × 32 × 53 = 36,000
22 × 3 × 55 = 37,500
29 × 3 × 52 = 38,400
26 × 54 = 40,000
23 × 32 × 54 = 45,000
3 × 56 = 46,875
27 × 3 × 53 = 48,000
24 × 55 = 50,000
2 × 32 × 55 = 56,250
28 × 32 × 52 = 57,600
25 × 3 × 54 = 60,000
22 × 56 = 62,500
29 × 53 = 64,000
26 × 32 × 53 = 72,000
23 × 3 × 55 = 75,000
57 = 78,125
27 × 54 = 80,000
24 × 32 × 54 = 90,000
2 × 3 × 56 = 93,750
28 × 3 × 53 = 96,000
25 × 55 = 100,000
22 × 32 × 55 = 112,500
29 × 32 × 52 = 115,200
26 × 3 × 54 = 120,000
23 × 56 = 125,000
32 × 56 = 140,625
27 × 32 × 53 = 144,000
24 × 3 × 55 = 150,000
2 × 57 = 156,250
28 × 54 = 160,000
25 × 32 × 54 = 180,000
22 × 3 × 56 = 187,500
29 × 3 × 53 = 192,000
26 × 55 = 200,000
23 × 32 × 55 = 225,000
3 × 57 = 234,375
27 × 3 × 54 = 240,000
24 × 56 = 250,000
2 × 32 × 56 = 281,250
28 × 32 × 53 = 288,000
25 × 3 × 55 = 300,000
22 × 57 = 312,500
29 × 54 = 320,000
26 × 32 × 54 = 360,000
23 × 3 × 56 = 375,000
27 × 55 = 400,000
24 × 32 × 55 = 450,000
2 × 3 × 57 = 468,750
28 × 3 × 54 = 480,000
25 × 56 = 500,000
22 × 32 × 56 = 562,500
29 × 32 × 53 = 576,000
26 × 3 × 55 = 600,000
23 × 57 = 625,000
32 × 57 = 703,125
27 × 32 × 54 = 720,000
24 × 3 × 56 = 750,000
28 × 55 = 800,000
25 × 32 × 55 = 900,000
22 × 3 × 57 = 937,500
29 × 3 × 54 = 960,000
26 × 56 = 1,000,000
23 × 32 × 56 = 1,125,000
27 × 3 × 55 = 1,200,000
24 × 57 = 1,250,000
2 × 32 × 57 = 1,406,250
28 × 32 × 54 = 1,440,000
25 × 3 × 56 = 1,500,000
29 × 55 = 1,600,000
26 × 32 × 55 = 1,800,000
23 × 3 × 57 = 1,875,000
27 × 56 = 2,000,000
24 × 32 × 56 = 2,250,000
28 × 3 × 55 = 2,400,000
25 × 57 = 2,500,000
22 × 32 × 57 = 2,812,500
29 × 32 × 54 = 2,880,000
26 × 3 × 56 = 3,000,000
27 × 32 × 55 = 3,600,000
24 × 3 × 57 = 3,750,000
28 × 56 = 4,000,000
25 × 32 × 56 = 4,500,000
29 × 3 × 55 = 4,800,000
26 × 57 = 5,000,000
23 × 32 × 57 = 5,625,000
27 × 3 × 56 = 6,000,000
28 × 32 × 55 = 7,200,000
25 × 3 × 57 = 7,500,000
29 × 56 = 8,000,000
26 × 32 × 56 = 9,000,000
27 × 57 = 10,000,000
24 × 32 × 57 = 11,250,000
28 × 3 × 56 = 12,000,000
29 × 32 × 55 = 14,400,000
26 × 3 × 57 = 15,000,000
27 × 32 × 56 = 18,000,000
28 × 57 = 20,000,000
25 × 32 × 57 = 22,500,000
29 × 3 × 56 = 24,000,000
27 × 3 × 57 = 30,000,000
28 × 32 × 56 = 36,000,000
29 × 57 = 40,000,000
26 × 32 × 57 = 45,000,000
28 × 3 × 57 = 60,000,000
29 × 32 × 56 = 72,000,000
27 × 32 × 57 = 90,000,000
29 × 3 × 57 = 120,000,000
28 × 32 × 57 = 180,000,000
29 × 32 × 57 = 360,000,000

The final answer:
(scroll down)

360,000,000 has 240 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 15; 16; 18; 20; 24; 25; 30; 32; 36; 40; 45; 48; 50; 60; 64; 72; 75; 80; 90; 96; 100; 120; 125; 128; 144; 150; 160; 180; 192; 200; 225; 240; 250; 256; 288; 300; 320; 360; 375; 384; 400; 450; 480; 500; 512; 576; 600; 625; 640; 720; 750; 768; 800; 900; 960; 1,000; 1,125; 1,152; 1,200; 1,250; 1,280; 1,440; 1,500; 1,536; 1,600; 1,800; 1,875; 1,920; 2,000; 2,250; 2,304; 2,400; 2,500; 2,560; 2,880; 3,000; 3,125; 3,200; 3,600; 3,750; 3,840; 4,000; 4,500; 4,608; 4,800; 5,000; 5,625; 5,760; 6,000; 6,250; 6,400; 7,200; 7,500; 7,680; 8,000; 9,000; 9,375; 9,600; 10,000; 11,250; 11,520; 12,000; 12,500; 12,800; 14,400; 15,000; 15,625; 16,000; 18,000; 18,750; 19,200; 20,000; 22,500; 23,040; 24,000; 25,000; 28,125; 28,800; 30,000; 31,250; 32,000; 36,000; 37,500; 38,400; 40,000; 45,000; 46,875; 48,000; 50,000; 56,250; 57,600; 60,000; 62,500; 64,000; 72,000; 75,000; 78,125; 80,000; 90,000; 93,750; 96,000; 100,000; 112,500; 115,200; 120,000; 125,000; 140,625; 144,000; 150,000; 156,250; 160,000; 180,000; 187,500; 192,000; 200,000; 225,000; 234,375; 240,000; 250,000; 281,250; 288,000; 300,000; 312,500; 320,000; 360,000; 375,000; 400,000; 450,000; 468,750; 480,000; 500,000; 562,500; 576,000; 600,000; 625,000; 703,125; 720,000; 750,000; 800,000; 900,000; 937,500; 960,000; 1,000,000; 1,125,000; 1,200,000; 1,250,000; 1,406,250; 1,440,000; 1,500,000; 1,600,000; 1,800,000; 1,875,000; 2,000,000; 2,250,000; 2,400,000; 2,500,000; 2,812,500; 2,880,000; 3,000,000; 3,600,000; 3,750,000; 4,000,000; 4,500,000; 4,800,000; 5,000,000; 5,625,000; 6,000,000; 7,200,000; 7,500,000; 8,000,000; 9,000,000; 10,000,000; 11,250,000; 12,000,000; 14,400,000; 15,000,000; 18,000,000; 20,000,000; 22,500,000; 24,000,000; 30,000,000; 36,000,000; 40,000,000; 45,000,000; 60,000,000; 72,000,000; 90,000,000; 120,000,000; 180,000,000 and 360,000,000
out of which 3 prime factors: 2; 3 and 5.
Numbers other than 1 that are not prime factors are composite factors (divisors).
360,000,000 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.

Similar operations of calculating common factors (divisors):

» Factors of 360,000,005. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

» Monthly Calculations: (Common) Factors (Divisors) of One or Two Numbers

» Month 11, 2025 [November]: Monthly Calculations: (Common) Factors (Divisors) of One or Two Numbers

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".