Given the Number 36,931,888, Calculate (Find) All the Factors (All the Divisors) of the Number 36,931,888 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 36,931,888

1. Carry out the prime factorization of the number 36,931,888:

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


36,931,888 = 24 × 72 × 172 × 163
36,931,888 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.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 36,931,888

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):

neither prime nor composite = 1
prime factor = 2
22 = 4
prime factor = 7
23 = 8
2 × 7 = 14
24 = 16
prime factor = 17
22 × 7 = 28
2 × 17 = 34
72 = 49
23 × 7 = 56
22 × 17 = 68
2 × 72 = 98
24 × 7 = 112
7 × 17 = 119
23 × 17 = 136
prime factor = 163
22 × 72 = 196
2 × 7 × 17 = 238
24 × 17 = 272
172 = 289
2 × 163 = 326
23 × 72 = 392
22 × 7 × 17 = 476
2 × 172 = 578
22 × 163 = 652
24 × 72 = 784
72 × 17 = 833
23 × 7 × 17 = 952
7 × 163 = 1,141
22 × 172 = 1,156
23 × 163 = 1,304
2 × 72 × 17 = 1,666
24 × 7 × 17 = 1,904
7 × 172 = 2,023
2 × 7 × 163 = 2,282
23 × 172 = 2,312
24 × 163 = 2,608
17 × 163 = 2,771
22 × 72 × 17 = 3,332
2 × 7 × 172 = 4,046
22 × 7 × 163 = 4,564
24 × 172 = 4,624
2 × 17 × 163 = 5,542
This list continues below...

... This list continues from above
23 × 72 × 17 = 6,664
72 × 163 = 7,987
22 × 7 × 172 = 8,092
23 × 7 × 163 = 9,128
22 × 17 × 163 = 11,084
24 × 72 × 17 = 13,328
72 × 172 = 14,161
2 × 72 × 163 = 15,974
23 × 7 × 172 = 16,184
24 × 7 × 163 = 18,256
7 × 17 × 163 = 19,397
23 × 17 × 163 = 22,168
2 × 72 × 172 = 28,322
22 × 72 × 163 = 31,948
24 × 7 × 172 = 32,368
2 × 7 × 17 × 163 = 38,794
24 × 17 × 163 = 44,336
172 × 163 = 47,107
22 × 72 × 172 = 56,644
23 × 72 × 163 = 63,896
22 × 7 × 17 × 163 = 77,588
2 × 172 × 163 = 94,214
23 × 72 × 172 = 113,288
24 × 72 × 163 = 127,792
72 × 17 × 163 = 135,779
23 × 7 × 17 × 163 = 155,176
22 × 172 × 163 = 188,428
24 × 72 × 172 = 226,576
2 × 72 × 17 × 163 = 271,558
24 × 7 × 17 × 163 = 310,352
7 × 172 × 163 = 329,749
23 × 172 × 163 = 376,856
22 × 72 × 17 × 163 = 543,116
2 × 7 × 172 × 163 = 659,498
24 × 172 × 163 = 753,712
23 × 72 × 17 × 163 = 1,086,232
22 × 7 × 172 × 163 = 1,318,996
24 × 72 × 17 × 163 = 2,172,464
72 × 172 × 163 = 2,308,243
23 × 7 × 172 × 163 = 2,637,992
2 × 72 × 172 × 163 = 4,616,486
24 × 7 × 172 × 163 = 5,275,984
22 × 72 × 172 × 163 = 9,232,972
23 × 72 × 172 × 163 = 18,465,944
24 × 72 × 172 × 163 = 36,931,888

The final answer:
(scroll down)

36,931,888 has 90 factors (divisors):
1; 2; 4; 7; 8; 14; 16; 17; 28; 34; 49; 56; 68; 98; 112; 119; 136; 163; 196; 238; 272; 289; 326; 392; 476; 578; 652; 784; 833; 952; 1,141; 1,156; 1,304; 1,666; 1,904; 2,023; 2,282; 2,312; 2,608; 2,771; 3,332; 4,046; 4,564; 4,624; 5,542; 6,664; 7,987; 8,092; 9,128; 11,084; 13,328; 14,161; 15,974; 16,184; 18,256; 19,397; 22,168; 28,322; 31,948; 32,368; 38,794; 44,336; 47,107; 56,644; 63,896; 77,588; 94,214; 113,288; 127,792; 135,779; 155,176; 188,428; 226,576; 271,558; 310,352; 329,749; 376,856; 543,116; 659,498; 753,712; 1,086,232; 1,318,996; 2,172,464; 2,308,243; 2,637,992; 4,616,486; 5,275,984; 9,232,972; 18,465,944 and 36,931,888
out of which 4 prime factors: 2; 7; 17 and 163
36,931,888 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.


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

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The list of all the calculated 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".