Given the Number 29,932,308, Calculate (Find) All the Factors (All the Divisors) of the Number 29,932,308 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 29,932,308

1. Carry out the prime factorization of the number 29,932,308:

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

29,932,308 = 22 × 33 × 7 × 172 × 137
29,932,308 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* 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 29,932,308

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
prime factor = 3
22 = 4
2 × 3 = 6
prime factor = 7
32 = 9
22 × 3 = 12
2 × 7 = 14
prime factor = 17
2 × 32 = 18
3 × 7 = 21
33 = 27
22 × 7 = 28
2 × 17 = 34
22 × 32 = 36
2 × 3 × 7 = 42
3 × 17 = 51
2 × 33 = 54
32 × 7 = 63
22 × 17 = 68
22 × 3 × 7 = 84
2 × 3 × 17 = 102
22 × 33 = 108
7 × 17 = 119
2 × 32 × 7 = 126
prime factor = 137
32 × 17 = 153
33 × 7 = 189
22 × 3 × 17 = 204
2 × 7 × 17 = 238
22 × 32 × 7 = 252
2 × 137 = 274
172 = 289
2 × 32 × 17 = 306
3 × 7 × 17 = 357
2 × 33 × 7 = 378
3 × 137 = 411
33 × 17 = 459
22 × 7 × 17 = 476
22 × 137 = 548
2 × 172 = 578
22 × 32 × 17 = 612
2 × 3 × 7 × 17 = 714
22 × 33 × 7 = 756
2 × 3 × 137 = 822
3 × 172 = 867
2 × 33 × 17 = 918
7 × 137 = 959
32 × 7 × 17 = 1,071
22 × 172 = 1,156
32 × 137 = 1,233
22 × 3 × 7 × 17 = 1,428
22 × 3 × 137 = 1,644
2 × 3 × 172 = 1,734
22 × 33 × 17 = 1,836
2 × 7 × 137 = 1,918
7 × 172 = 2,023
2 × 32 × 7 × 17 = 2,142
17 × 137 = 2,329
2 × 32 × 137 = 2,466
32 × 172 = 2,601
3 × 7 × 137 = 2,877
33 × 7 × 17 = 3,213
22 × 3 × 172 = 3,468
33 × 137 = 3,699
22 × 7 × 137 = 3,836
2 × 7 × 172 = 4,046
22 × 32 × 7 × 17 = 4,284
2 × 17 × 137 = 4,658
22 × 32 × 137 = 4,932
2 × 32 × 172 = 5,202
This list continues below...

... This list continues from above
2 × 3 × 7 × 137 = 5,754
3 × 7 × 172 = 6,069
2 × 33 × 7 × 17 = 6,426
3 × 17 × 137 = 6,987
2 × 33 × 137 = 7,398
33 × 172 = 7,803
22 × 7 × 172 = 8,092
32 × 7 × 137 = 8,631
22 × 17 × 137 = 9,316
22 × 32 × 172 = 10,404
22 × 3 × 7 × 137 = 11,508
2 × 3 × 7 × 172 = 12,138
22 × 33 × 7 × 17 = 12,852
2 × 3 × 17 × 137 = 13,974
22 × 33 × 137 = 14,796
2 × 33 × 172 = 15,606
7 × 17 × 137 = 16,303
2 × 32 × 7 × 137 = 17,262
32 × 7 × 172 = 18,207
32 × 17 × 137 = 20,961
22 × 3 × 7 × 172 = 24,276
33 × 7 × 137 = 25,893
22 × 3 × 17 × 137 = 27,948
22 × 33 × 172 = 31,212
2 × 7 × 17 × 137 = 32,606
22 × 32 × 7 × 137 = 34,524
2 × 32 × 7 × 172 = 36,414
172 × 137 = 39,593
2 × 32 × 17 × 137 = 41,922
3 × 7 × 17 × 137 = 48,909
2 × 33 × 7 × 137 = 51,786
33 × 7 × 172 = 54,621
33 × 17 × 137 = 62,883
22 × 7 × 17 × 137 = 65,212
22 × 32 × 7 × 172 = 72,828
2 × 172 × 137 = 79,186
22 × 32 × 17 × 137 = 83,844
2 × 3 × 7 × 17 × 137 = 97,818
22 × 33 × 7 × 137 = 103,572
2 × 33 × 7 × 172 = 109,242
3 × 172 × 137 = 118,779
2 × 33 × 17 × 137 = 125,766
32 × 7 × 17 × 137 = 146,727
22 × 172 × 137 = 158,372
22 × 3 × 7 × 17 × 137 = 195,636
22 × 33 × 7 × 172 = 218,484
2 × 3 × 172 × 137 = 237,558
22 × 33 × 17 × 137 = 251,532
7 × 172 × 137 = 277,151
2 × 32 × 7 × 17 × 137 = 293,454
32 × 172 × 137 = 356,337
33 × 7 × 17 × 137 = 440,181
22 × 3 × 172 × 137 = 475,116
2 × 7 × 172 × 137 = 554,302
22 × 32 × 7 × 17 × 137 = 586,908
2 × 32 × 172 × 137 = 712,674
3 × 7 × 172 × 137 = 831,453
2 × 33 × 7 × 17 × 137 = 880,362
33 × 172 × 137 = 1,069,011
22 × 7 × 172 × 137 = 1,108,604
22 × 32 × 172 × 137 = 1,425,348
2 × 3 × 7 × 172 × 137 = 1,662,906
22 × 33 × 7 × 17 × 137 = 1,760,724
2 × 33 × 172 × 137 = 2,138,022
32 × 7 × 172 × 137 = 2,494,359
22 × 3 × 7 × 172 × 137 = 3,325,812
22 × 33 × 172 × 137 = 4,276,044
2 × 32 × 7 × 172 × 137 = 4,988,718
33 × 7 × 172 × 137 = 7,483,077
22 × 32 × 7 × 172 × 137 = 9,977,436
2 × 33 × 7 × 172 × 137 = 14,966,154
22 × 33 × 7 × 172 × 137 = 29,932,308

The final answer:
(scroll down)

29,932,308 has 144 factors (divisors):
1; 2; 3; 4; 6; 7; 9; 12; 14; 17; 18; 21; 27; 28; 34; 36; 42; 51; 54; 63; 68; 84; 102; 108; 119; 126; 137; 153; 189; 204; 238; 252; 274; 289; 306; 357; 378; 411; 459; 476; 548; 578; 612; 714; 756; 822; 867; 918; 959; 1,071; 1,156; 1,233; 1,428; 1,644; 1,734; 1,836; 1,918; 2,023; 2,142; 2,329; 2,466; 2,601; 2,877; 3,213; 3,468; 3,699; 3,836; 4,046; 4,284; 4,658; 4,932; 5,202; 5,754; 6,069; 6,426; 6,987; 7,398; 7,803; 8,092; 8,631; 9,316; 10,404; 11,508; 12,138; 12,852; 13,974; 14,796; 15,606; 16,303; 17,262; 18,207; 20,961; 24,276; 25,893; 27,948; 31,212; 32,606; 34,524; 36,414; 39,593; 41,922; 48,909; 51,786; 54,621; 62,883; 65,212; 72,828; 79,186; 83,844; 97,818; 103,572; 109,242; 118,779; 125,766; 146,727; 158,372; 195,636; 218,484; 237,558; 251,532; 277,151; 293,454; 356,337; 440,181; 475,116; 554,302; 586,908; 712,674; 831,453; 880,362; 1,069,011; 1,108,604; 1,425,348; 1,662,906; 1,760,724; 2,138,022; 2,494,359; 3,325,812; 4,276,044; 4,988,718; 7,483,077; 9,977,436; 14,966,154 and 29,932,308
out of which 5 prime factors: 2; 3; 7; 17 and 137
29,932,308 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.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 29,932,297?

» What are all the proper, improper and prime factors (divisors) of the number 29,932,310?


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.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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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".