Given the Number 36,323,196, Calculate (Find) All the Factors (All the Divisors) of the Number 36,323,196 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 36,323,196

1. Carry out the prime factorization of the number 36,323,196:

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


36,323,196 = 22 × 3 × 7 × 13 × 29 × 31 × 37
36,323,196 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 36,323,196

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
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 7 = 21
2 × 13 = 26
22 × 7 = 28
prime factor = 29
prime factor = 31
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
22 × 13 = 52
2 × 29 = 58
2 × 31 = 62
2 × 37 = 74
2 × 3 × 13 = 78
22 × 3 × 7 = 84
3 × 29 = 87
7 × 13 = 91
3 × 31 = 93
3 × 37 = 111
22 × 29 = 116
22 × 31 = 124
22 × 37 = 148
22 × 3 × 13 = 156
2 × 3 × 29 = 174
2 × 7 × 13 = 182
2 × 3 × 31 = 186
7 × 29 = 203
7 × 31 = 217
2 × 3 × 37 = 222
7 × 37 = 259
3 × 7 × 13 = 273
22 × 3 × 29 = 348
22 × 7 × 13 = 364
22 × 3 × 31 = 372
13 × 29 = 377
13 × 31 = 403
2 × 7 × 29 = 406
2 × 7 × 31 = 434
22 × 3 × 37 = 444
13 × 37 = 481
2 × 7 × 37 = 518
2 × 3 × 7 × 13 = 546
3 × 7 × 29 = 609
3 × 7 × 31 = 651
2 × 13 × 29 = 754
3 × 7 × 37 = 777
2 × 13 × 31 = 806
22 × 7 × 29 = 812
22 × 7 × 31 = 868
29 × 31 = 899
2 × 13 × 37 = 962
22 × 7 × 37 = 1,036
29 × 37 = 1,073
22 × 3 × 7 × 13 = 1,092
3 × 13 × 29 = 1,131
31 × 37 = 1,147
3 × 13 × 31 = 1,209
2 × 3 × 7 × 29 = 1,218
2 × 3 × 7 × 31 = 1,302
3 × 13 × 37 = 1,443
22 × 13 × 29 = 1,508
2 × 3 × 7 × 37 = 1,554
22 × 13 × 31 = 1,612
2 × 29 × 31 = 1,798
22 × 13 × 37 = 1,924
2 × 29 × 37 = 2,146
2 × 3 × 13 × 29 = 2,262
2 × 31 × 37 = 2,294
2 × 3 × 13 × 31 = 2,418
22 × 3 × 7 × 29 = 2,436
22 × 3 × 7 × 31 = 2,604
7 × 13 × 29 = 2,639
3 × 29 × 31 = 2,697
7 × 13 × 31 = 2,821
2 × 3 × 13 × 37 = 2,886
22 × 3 × 7 × 37 = 3,108
3 × 29 × 37 = 3,219
7 × 13 × 37 = 3,367
3 × 31 × 37 = 3,441
22 × 29 × 31 = 3,596
22 × 29 × 37 = 4,292
22 × 3 × 13 × 29 = 4,524
22 × 31 × 37 = 4,588
22 × 3 × 13 × 31 = 4,836
2 × 7 × 13 × 29 = 5,278
2 × 3 × 29 × 31 = 5,394
2 × 7 × 13 × 31 = 5,642
22 × 3 × 13 × 37 = 5,772
This list continues below...

... This list continues from above
7 × 29 × 31 = 6,293
2 × 3 × 29 × 37 = 6,438
2 × 7 × 13 × 37 = 6,734
2 × 3 × 31 × 37 = 6,882
7 × 29 × 37 = 7,511
3 × 7 × 13 × 29 = 7,917
7 × 31 × 37 = 8,029
3 × 7 × 13 × 31 = 8,463
3 × 7 × 13 × 37 = 10,101
22 × 7 × 13 × 29 = 10,556
22 × 3 × 29 × 31 = 10,788
22 × 7 × 13 × 31 = 11,284
13 × 29 × 31 = 11,687
2 × 7 × 29 × 31 = 12,586
22 × 3 × 29 × 37 = 12,876
22 × 7 × 13 × 37 = 13,468
22 × 3 × 31 × 37 = 13,764
13 × 29 × 37 = 13,949
13 × 31 × 37 = 14,911
2 × 7 × 29 × 37 = 15,022
2 × 3 × 7 × 13 × 29 = 15,834
2 × 7 × 31 × 37 = 16,058
2 × 3 × 7 × 13 × 31 = 16,926
3 × 7 × 29 × 31 = 18,879
2 × 3 × 7 × 13 × 37 = 20,202
3 × 7 × 29 × 37 = 22,533
2 × 13 × 29 × 31 = 23,374
3 × 7 × 31 × 37 = 24,087
22 × 7 × 29 × 31 = 25,172
2 × 13 × 29 × 37 = 27,898
2 × 13 × 31 × 37 = 29,822
22 × 7 × 29 × 37 = 30,044
22 × 3 × 7 × 13 × 29 = 31,668
22 × 7 × 31 × 37 = 32,116
29 × 31 × 37 = 33,263
22 × 3 × 7 × 13 × 31 = 33,852
3 × 13 × 29 × 31 = 35,061
2 × 3 × 7 × 29 × 31 = 37,758
22 × 3 × 7 × 13 × 37 = 40,404
3 × 13 × 29 × 37 = 41,847
3 × 13 × 31 × 37 = 44,733
2 × 3 × 7 × 29 × 37 = 45,066
22 × 13 × 29 × 31 = 46,748
2 × 3 × 7 × 31 × 37 = 48,174
22 × 13 × 29 × 37 = 55,796
22 × 13 × 31 × 37 = 59,644
2 × 29 × 31 × 37 = 66,526
2 × 3 × 13 × 29 × 31 = 70,122
22 × 3 × 7 × 29 × 31 = 75,516
7 × 13 × 29 × 31 = 81,809
2 × 3 × 13 × 29 × 37 = 83,694
2 × 3 × 13 × 31 × 37 = 89,466
22 × 3 × 7 × 29 × 37 = 90,132
22 × 3 × 7 × 31 × 37 = 96,348
7 × 13 × 29 × 37 = 97,643
3 × 29 × 31 × 37 = 99,789
7 × 13 × 31 × 37 = 104,377
22 × 29 × 31 × 37 = 133,052
22 × 3 × 13 × 29 × 31 = 140,244
2 × 7 × 13 × 29 × 31 = 163,618
22 × 3 × 13 × 29 × 37 = 167,388
22 × 3 × 13 × 31 × 37 = 178,932
2 × 7 × 13 × 29 × 37 = 195,286
2 × 3 × 29 × 31 × 37 = 199,578
2 × 7 × 13 × 31 × 37 = 208,754
7 × 29 × 31 × 37 = 232,841
3 × 7 × 13 × 29 × 31 = 245,427
3 × 7 × 13 × 29 × 37 = 292,929
3 × 7 × 13 × 31 × 37 = 313,131
22 × 7 × 13 × 29 × 31 = 327,236
22 × 7 × 13 × 29 × 37 = 390,572
22 × 3 × 29 × 31 × 37 = 399,156
22 × 7 × 13 × 31 × 37 = 417,508
13 × 29 × 31 × 37 = 432,419
2 × 7 × 29 × 31 × 37 = 465,682
2 × 3 × 7 × 13 × 29 × 31 = 490,854
2 × 3 × 7 × 13 × 29 × 37 = 585,858
2 × 3 × 7 × 13 × 31 × 37 = 626,262
3 × 7 × 29 × 31 × 37 = 698,523
2 × 13 × 29 × 31 × 37 = 864,838
22 × 7 × 29 × 31 × 37 = 931,364
22 × 3 × 7 × 13 × 29 × 31 = 981,708
22 × 3 × 7 × 13 × 29 × 37 = 1,171,716
22 × 3 × 7 × 13 × 31 × 37 = 1,252,524
3 × 13 × 29 × 31 × 37 = 1,297,257
2 × 3 × 7 × 29 × 31 × 37 = 1,397,046
22 × 13 × 29 × 31 × 37 = 1,729,676
2 × 3 × 13 × 29 × 31 × 37 = 2,594,514
22 × 3 × 7 × 29 × 31 × 37 = 2,794,092
7 × 13 × 29 × 31 × 37 = 3,026,933
22 × 3 × 13 × 29 × 31 × 37 = 5,189,028
2 × 7 × 13 × 29 × 31 × 37 = 6,053,866
3 × 7 × 13 × 29 × 31 × 37 = 9,080,799
22 × 7 × 13 × 29 × 31 × 37 = 12,107,732
2 × 3 × 7 × 13 × 29 × 31 × 37 = 18,161,598
22 × 3 × 7 × 13 × 29 × 31 × 37 = 36,323,196

The final answer:
(scroll down)

36,323,196 has 192 factors (divisors):
1; 2; 3; 4; 6; 7; 12; 13; 14; 21; 26; 28; 29; 31; 37; 39; 42; 52; 58; 62; 74; 78; 84; 87; 91; 93; 111; 116; 124; 148; 156; 174; 182; 186; 203; 217; 222; 259; 273; 348; 364; 372; 377; 403; 406; 434; 444; 481; 518; 546; 609; 651; 754; 777; 806; 812; 868; 899; 962; 1,036; 1,073; 1,092; 1,131; 1,147; 1,209; 1,218; 1,302; 1,443; 1,508; 1,554; 1,612; 1,798; 1,924; 2,146; 2,262; 2,294; 2,418; 2,436; 2,604; 2,639; 2,697; 2,821; 2,886; 3,108; 3,219; 3,367; 3,441; 3,596; 4,292; 4,524; 4,588; 4,836; 5,278; 5,394; 5,642; 5,772; 6,293; 6,438; 6,734; 6,882; 7,511; 7,917; 8,029; 8,463; 10,101; 10,556; 10,788; 11,284; 11,687; 12,586; 12,876; 13,468; 13,764; 13,949; 14,911; 15,022; 15,834; 16,058; 16,926; 18,879; 20,202; 22,533; 23,374; 24,087; 25,172; 27,898; 29,822; 30,044; 31,668; 32,116; 33,263; 33,852; 35,061; 37,758; 40,404; 41,847; 44,733; 45,066; 46,748; 48,174; 55,796; 59,644; 66,526; 70,122; 75,516; 81,809; 83,694; 89,466; 90,132; 96,348; 97,643; 99,789; 104,377; 133,052; 140,244; 163,618; 167,388; 178,932; 195,286; 199,578; 208,754; 232,841; 245,427; 292,929; 313,131; 327,236; 390,572; 399,156; 417,508; 432,419; 465,682; 490,854; 585,858; 626,262; 698,523; 864,838; 931,364; 981,708; 1,171,716; 1,252,524; 1,297,257; 1,397,046; 1,729,676; 2,594,514; 2,794,092; 3,026,933; 5,189,028; 6,053,866; 9,080,799; 12,107,732; 18,161,598 and 36,323,196
out of which 7 prime factors: 2; 3; 7; 13; 29; 31 and 37
36,323,196 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.

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".