Factors of 365,040. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 365,040. Connection with the prime factorization of the number

To find all the divisors of the number 365,040:

  • 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 365,040:

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


365,040 = 24 × 33 × 5 × 132
365,040 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) × (3 + 1) × (1 + 1) × (2 + 1) = 5 × 4 × 2 × 3 = 120

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

2. Multiply the prime factors of the number 365,040

  • 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
composite factor = 23 = 8
composite factor = 32 = 9
composite factor = 2 × 5 = 10
composite factor = 22 × 3 = 12
prime factor = 13
composite factor = 3 × 5 = 15
composite factor = 24 = 16
composite factor = 2 × 32 = 18
composite factor = 22 × 5 = 20
composite factor = 23 × 3 = 24
composite factor = 2 × 13 = 26
composite factor = 33 = 27
composite factor = 2 × 3 × 5 = 30
composite factor = 22 × 32 = 36
composite factor = 3 × 13 = 39
composite factor = 23 × 5 = 40
composite factor = 32 × 5 = 45
composite factor = 24 × 3 = 48
composite factor = 22 × 13 = 52
composite factor = 2 × 33 = 54
composite factor = 22 × 3 × 5 = 60
composite factor = 5 × 13 = 65
composite factor = 23 × 32 = 72
composite factor = 2 × 3 × 13 = 78
composite factor = 24 × 5 = 80
composite factor = 2 × 32 × 5 = 90
composite factor = 23 × 13 = 104
composite factor = 22 × 33 = 108
composite factor = 32 × 13 = 117
composite factor = 23 × 3 × 5 = 120
composite factor = 2 × 5 × 13 = 130
composite factor = 33 × 5 = 135
composite factor = 24 × 32 = 144
composite factor = 22 × 3 × 13 = 156
composite factor = 132 = 169
composite factor = 22 × 32 × 5 = 180
composite factor = 3 × 5 × 13 = 195
composite factor = 24 × 13 = 208
composite factor = 23 × 33 = 216
composite factor = 2 × 32 × 13 = 234
composite factor = 24 × 3 × 5 = 240
composite factor = 22 × 5 × 13 = 260
composite factor = 2 × 33 × 5 = 270
composite factor = 23 × 3 × 13 = 312
composite factor = 2 × 132 = 338
composite factor = 33 × 13 = 351
composite factor = 23 × 32 × 5 = 360
composite factor = 2 × 3 × 5 × 13 = 390
composite factor = 24 × 33 = 432
composite factor = 22 × 32 × 13 = 468
composite factor = 3 × 132 = 507
composite factor = 23 × 5 × 13 = 520
composite factor = 22 × 33 × 5 = 540
composite factor = 32 × 5 × 13 = 585
This list continues below...

... This list continues from above
composite factor = 24 × 3 × 13 = 624
composite factor = 22 × 132 = 676
composite factor = 2 × 33 × 13 = 702
composite factor = 24 × 32 × 5 = 720
composite factor = 22 × 3 × 5 × 13 = 780
composite factor = 5 × 132 = 845
composite factor = 23 × 32 × 13 = 936
composite factor = 2 × 3 × 132 = 1,014
composite factor = 24 × 5 × 13 = 1,040
composite factor = 23 × 33 × 5 = 1,080
composite factor = 2 × 32 × 5 × 13 = 1,170
composite factor = 23 × 132 = 1,352
composite factor = 22 × 33 × 13 = 1,404
composite factor = 32 × 132 = 1,521
composite factor = 23 × 3 × 5 × 13 = 1,560
composite factor = 2 × 5 × 132 = 1,690
composite factor = 33 × 5 × 13 = 1,755
composite factor = 24 × 32 × 13 = 1,872
composite factor = 22 × 3 × 132 = 2,028
composite factor = 24 × 33 × 5 = 2,160
composite factor = 22 × 32 × 5 × 13 = 2,340
composite factor = 3 × 5 × 132 = 2,535
composite factor = 24 × 132 = 2,704
composite factor = 23 × 33 × 13 = 2,808
composite factor = 2 × 32 × 132 = 3,042
composite factor = 24 × 3 × 5 × 13 = 3,120
composite factor = 22 × 5 × 132 = 3,380
composite factor = 2 × 33 × 5 × 13 = 3,510
composite factor = 23 × 3 × 132 = 4,056
composite factor = 33 × 132 = 4,563
composite factor = 23 × 32 × 5 × 13 = 4,680
composite factor = 2 × 3 × 5 × 132 = 5,070
composite factor = 24 × 33 × 13 = 5,616
composite factor = 22 × 32 × 132 = 6,084
composite factor = 23 × 5 × 132 = 6,760
composite factor = 22 × 33 × 5 × 13 = 7,020
composite factor = 32 × 5 × 132 = 7,605
composite factor = 24 × 3 × 132 = 8,112
composite factor = 2 × 33 × 132 = 9,126
composite factor = 24 × 32 × 5 × 13 = 9,360
composite factor = 22 × 3 × 5 × 132 = 10,140
composite factor = 23 × 32 × 132 = 12,168
composite factor = 24 × 5 × 132 = 13,520
composite factor = 23 × 33 × 5 × 13 = 14,040
composite factor = 2 × 32 × 5 × 132 = 15,210
composite factor = 22 × 33 × 132 = 18,252
composite factor = 23 × 3 × 5 × 132 = 20,280
composite factor = 33 × 5 × 132 = 22,815
composite factor = 24 × 32 × 132 = 24,336
composite factor = 24 × 33 × 5 × 13 = 28,080
composite factor = 22 × 32 × 5 × 132 = 30,420
composite factor = 23 × 33 × 132 = 36,504
composite factor = 24 × 3 × 5 × 132 = 40,560
composite factor = 2 × 33 × 5 × 132 = 45,630
composite factor = 23 × 32 × 5 × 132 = 60,840
composite factor = 24 × 33 × 132 = 73,008
composite factor = 22 × 33 × 5 × 132 = 91,260
composite factor = 24 × 32 × 5 × 132 = 121,680
composite factor = 23 × 33 × 5 × 132 = 182,520
composite factor = 24 × 33 × 5 × 132 = 365,040
120 factors (divisors)

What times what is 365,040?
What number multiplied by what number equals 365,040?

All the combinations of any two natural numbers whose product equals 365,040.

1 × 365,040 = 365,040
2 × 182,520 = 365,040
3 × 121,680 = 365,040
4 × 91,260 = 365,040
5 × 73,008 = 365,040
6 × 60,840 = 365,040
8 × 45,630 = 365,040
9 × 40,560 = 365,040
10 × 36,504 = 365,040
12 × 30,420 = 365,040
13 × 28,080 = 365,040
15 × 24,336 = 365,040
16 × 22,815 = 365,040
18 × 20,280 = 365,040
20 × 18,252 = 365,040
24 × 15,210 = 365,040
26 × 14,040 = 365,040
27 × 13,520 = 365,040
30 × 12,168 = 365,040
36 × 10,140 = 365,040
39 × 9,360 = 365,040
40 × 9,126 = 365,040
45 × 8,112 = 365,040
48 × 7,605 = 365,040
52 × 7,020 = 365,040
54 × 6,760 = 365,040
60 × 6,084 = 365,040
65 × 5,616 = 365,040
72 × 5,070 = 365,040
78 × 4,680 = 365,040
80 × 4,563 = 365,040
90 × 4,056 = 365,040
104 × 3,510 = 365,040
108 × 3,380 = 365,040
117 × 3,120 = 365,040
120 × 3,042 = 365,040
130 × 2,808 = 365,040
135 × 2,704 = 365,040
144 × 2,535 = 365,040
156 × 2,340 = 365,040
169 × 2,160 = 365,040
180 × 2,028 = 365,040
195 × 1,872 = 365,040
208 × 1,755 = 365,040
216 × 1,690 = 365,040
234 × 1,560 = 365,040
240 × 1,521 = 365,040
260 × 1,404 = 365,040
270 × 1,352 = 365,040
312 × 1,170 = 365,040
338 × 1,080 = 365,040
351 × 1,040 = 365,040
360 × 1,014 = 365,040
390 × 936 = 365,040
432 × 845 = 365,040
468 × 780 = 365,040
507 × 720 = 365,040
520 × 702 = 365,040
540 × 676 = 365,040
585 × 624 = 365,040
60 unique multiplications

The final answer:
(scroll down)


365,040 has 120 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 13; 15; 16; 18; 20; 24; 26; 27; 30; 36; 39; 40; 45; 48; 52; 54; 60; 65; 72; 78; 80; 90; 104; 108; 117; 120; 130; 135; 144; 156; 169; 180; 195; 208; 216; 234; 240; 260; 270; 312; 338; 351; 360; 390; 432; 468; 507; 520; 540; 585; 624; 676; 702; 720; 780; 845; 936; 1,014; 1,040; 1,080; 1,170; 1,352; 1,404; 1,521; 1,560; 1,690; 1,755; 1,872; 2,028; 2,160; 2,340; 2,535; 2,704; 2,808; 3,042; 3,120; 3,380; 3,510; 4,056; 4,563; 4,680; 5,070; 5,616; 6,084; 6,760; 7,020; 7,605; 8,112; 9,126; 9,360; 10,140; 12,168; 13,520; 14,040; 15,210; 18,252; 20,280; 22,815; 24,336; 28,080; 30,420; 36,504; 40,560; 45,630; 60,840; 73,008; 91,260; 121,680; 182,520 and 365,040
out of which 4 prime factors: 2; 3; 5 and 13.
Numbers other than 1 that are not prime factors are composite factors (divisors).
365,040 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".