Given the Number 11,999,988 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 11,999,988

1. Carry out the prime factorization of the number 11,999,988:

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


11,999,988 = 22 × 34 × 7 × 11 × 13 × 37
11,999,988 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 11,999,988

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
prime factor = 11
22 × 3 = 12
prime factor = 13
2 × 7 = 14
2 × 32 = 18
3 × 7 = 21
2 × 11 = 22
2 × 13 = 26
33 = 27
22 × 7 = 28
3 × 11 = 33
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
22 × 11 = 44
22 × 13 = 52
2 × 33 = 54
32 × 7 = 63
2 × 3 × 11 = 66
2 × 37 = 74
7 × 11 = 77
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
7 × 13 = 91
32 × 11 = 99
22 × 33 = 108
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
22 × 3 × 11 = 132
11 × 13 = 143
22 × 37 = 148
2 × 7 × 11 = 154
22 × 3 × 13 = 156
2 × 34 = 162
2 × 7 × 13 = 182
33 × 7 = 189
2 × 32 × 11 = 198
2 × 3 × 37 = 222
3 × 7 × 11 = 231
2 × 32 × 13 = 234
22 × 32 × 7 = 252
7 × 37 = 259
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
22 × 7 × 11 = 308
22 × 34 = 324
32 × 37 = 333
33 × 13 = 351
22 × 7 × 13 = 364
2 × 33 × 7 = 378
22 × 32 × 11 = 396
11 × 37 = 407
3 × 11 × 13 = 429
22 × 3 × 37 = 444
2 × 3 × 7 × 11 = 462
22 × 32 × 13 = 468
13 × 37 = 481
2 × 7 × 37 = 518
2 × 3 × 7 × 13 = 546
34 × 7 = 567
22 × 11 × 13 = 572
2 × 33 × 11 = 594
2 × 32 × 37 = 666
32 × 7 × 11 = 693
2 × 33 × 13 = 702
22 × 33 × 7 = 756
3 × 7 × 37 = 777
2 × 11 × 37 = 814
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
34 × 11 = 891
22 × 3 × 7 × 11 = 924
2 × 13 × 37 = 962
33 × 37 = 999
7 × 11 × 13 = 1,001
22 × 7 × 37 = 1,036
34 × 13 = 1,053
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
22 × 33 × 11 = 1,188
3 × 11 × 37 = 1,221
32 × 11 × 13 = 1,287
22 × 32 × 37 = 1,332
2 × 32 × 7 × 11 = 1,386
22 × 33 × 13 = 1,404
3 × 13 × 37 = 1,443
2 × 3 × 7 × 37 = 1,554
22 × 11 × 37 = 1,628
2 × 32 × 7 × 13 = 1,638
22 × 3 × 11 × 13 = 1,716
2 × 34 × 11 = 1,782
22 × 13 × 37 = 1,924
2 × 33 × 37 = 1,998
2 × 7 × 11 × 13 = 2,002
33 × 7 × 11 = 2,079
2 × 34 × 13 = 2,106
22 × 34 × 7 = 2,268
32 × 7 × 37 = 2,331
2 × 3 × 11 × 37 = 2,442
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
22 × 32 × 7 × 11 = 2,772
7 × 11 × 37 = 2,849
2 × 3 × 13 × 37 = 2,886
34 × 37 = 2,997
3 × 7 × 11 × 13 = 3,003
22 × 3 × 7 × 37 = 3,108
22 × 32 × 7 × 13 = 3,276
7 × 13 × 37 = 3,367
This list continues below...

... This list continues from above
22 × 34 × 11 = 3,564
32 × 11 × 37 = 3,663
33 × 11 × 13 = 3,861
22 × 33 × 37 = 3,996
22 × 7 × 11 × 13 = 4,004
2 × 33 × 7 × 11 = 4,158
22 × 34 × 13 = 4,212
32 × 13 × 37 = 4,329
2 × 32 × 7 × 37 = 4,662
22 × 3 × 11 × 37 = 4,884
2 × 33 × 7 × 13 = 4,914
22 × 32 × 11 × 13 = 5,148
11 × 13 × 37 = 5,291
2 × 7 × 11 × 37 = 5,698
22 × 3 × 13 × 37 = 5,772
2 × 34 × 37 = 5,994
2 × 3 × 7 × 11 × 13 = 6,006
34 × 7 × 11 = 6,237
2 × 7 × 13 × 37 = 6,734
33 × 7 × 37 = 6,993
2 × 32 × 11 × 37 = 7,326
34 × 7 × 13 = 7,371
2 × 33 × 11 × 13 = 7,722
22 × 33 × 7 × 11 = 8,316
3 × 7 × 11 × 37 = 8,547
2 × 32 × 13 × 37 = 8,658
32 × 7 × 11 × 13 = 9,009
22 × 32 × 7 × 37 = 9,324
22 × 33 × 7 × 13 = 9,828
3 × 7 × 13 × 37 = 10,101
2 × 11 × 13 × 37 = 10,582
33 × 11 × 37 = 10,989
22 × 7 × 11 × 37 = 11,396
34 × 11 × 13 = 11,583
22 × 34 × 37 = 11,988
22 × 3 × 7 × 11 × 13 = 12,012
2 × 34 × 7 × 11 = 12,474
33 × 13 × 37 = 12,987
22 × 7 × 13 × 37 = 13,468
2 × 33 × 7 × 37 = 13,986
22 × 32 × 11 × 37 = 14,652
2 × 34 × 7 × 13 = 14,742
22 × 33 × 11 × 13 = 15,444
3 × 11 × 13 × 37 = 15,873
2 × 3 × 7 × 11 × 37 = 17,094
22 × 32 × 13 × 37 = 17,316
2 × 32 × 7 × 11 × 13 = 18,018
2 × 3 × 7 × 13 × 37 = 20,202
34 × 7 × 37 = 20,979
22 × 11 × 13 × 37 = 21,164
2 × 33 × 11 × 37 = 21,978
2 × 34 × 11 × 13 = 23,166
22 × 34 × 7 × 11 = 24,948
32 × 7 × 11 × 37 = 25,641
2 × 33 × 13 × 37 = 25,974
33 × 7 × 11 × 13 = 27,027
22 × 33 × 7 × 37 = 27,972
22 × 34 × 7 × 13 = 29,484
32 × 7 × 13 × 37 = 30,303
2 × 3 × 11 × 13 × 37 = 31,746
34 × 11 × 37 = 32,967
22 × 3 × 7 × 11 × 37 = 34,188
22 × 32 × 7 × 11 × 13 = 36,036
7 × 11 × 13 × 37 = 37,037
34 × 13 × 37 = 38,961
22 × 3 × 7 × 13 × 37 = 40,404
2 × 34 × 7 × 37 = 41,958
22 × 33 × 11 × 37 = 43,956
22 × 34 × 11 × 13 = 46,332
32 × 11 × 13 × 37 = 47,619
2 × 32 × 7 × 11 × 37 = 51,282
22 × 33 × 13 × 37 = 51,948
2 × 33 × 7 × 11 × 13 = 54,054
2 × 32 × 7 × 13 × 37 = 60,606
22 × 3 × 11 × 13 × 37 = 63,492
2 × 34 × 11 × 37 = 65,934
2 × 7 × 11 × 13 × 37 = 74,074
33 × 7 × 11 × 37 = 76,923
2 × 34 × 13 × 37 = 77,922
34 × 7 × 11 × 13 = 81,081
22 × 34 × 7 × 37 = 83,916
33 × 7 × 13 × 37 = 90,909
2 × 32 × 11 × 13 × 37 = 95,238
22 × 32 × 7 × 11 × 37 = 102,564
22 × 33 × 7 × 11 × 13 = 108,108
3 × 7 × 11 × 13 × 37 = 111,111
22 × 32 × 7 × 13 × 37 = 121,212
22 × 34 × 11 × 37 = 131,868
33 × 11 × 13 × 37 = 142,857
22 × 7 × 11 × 13 × 37 = 148,148
2 × 33 × 7 × 11 × 37 = 153,846
22 × 34 × 13 × 37 = 155,844
2 × 34 × 7 × 11 × 13 = 162,162
2 × 33 × 7 × 13 × 37 = 181,818
22 × 32 × 11 × 13 × 37 = 190,476
2 × 3 × 7 × 11 × 13 × 37 = 222,222
34 × 7 × 11 × 37 = 230,769
34 × 7 × 13 × 37 = 272,727
2 × 33 × 11 × 13 × 37 = 285,714
22 × 33 × 7 × 11 × 37 = 307,692
22 × 34 × 7 × 11 × 13 = 324,324
32 × 7 × 11 × 13 × 37 = 333,333
22 × 33 × 7 × 13 × 37 = 363,636
34 × 11 × 13 × 37 = 428,571
22 × 3 × 7 × 11 × 13 × 37 = 444,444
2 × 34 × 7 × 11 × 37 = 461,538
2 × 34 × 7 × 13 × 37 = 545,454
22 × 33 × 11 × 13 × 37 = 571,428
2 × 32 × 7 × 11 × 13 × 37 = 666,666
2 × 34 × 11 × 13 × 37 = 857,142
22 × 34 × 7 × 11 × 37 = 923,076
33 × 7 × 11 × 13 × 37 = 999,999
22 × 34 × 7 × 13 × 37 = 1,090,908
22 × 32 × 7 × 11 × 13 × 37 = 1,333,332
22 × 34 × 11 × 13 × 37 = 1,714,284
2 × 33 × 7 × 11 × 13 × 37 = 1,999,998
34 × 7 × 11 × 13 × 37 = 2,999,997
22 × 33 × 7 × 11 × 13 × 37 = 3,999,996
2 × 34 × 7 × 11 × 13 × 37 = 5,999,994
22 × 34 × 7 × 11 × 13 × 37 = 11,999,988

The final answer:
(scroll down)

11,999,988 has 240 factors (divisors):
1; 2; 3; 4; 6; 7; 9; 11; 12; 13; 14; 18; 21; 22; 26; 27; 28; 33; 36; 37; 39; 42; 44; 52; 54; 63; 66; 74; 77; 78; 81; 84; 91; 99; 108; 111; 117; 126; 132; 143; 148; 154; 156; 162; 182; 189; 198; 222; 231; 234; 252; 259; 273; 286; 297; 308; 324; 333; 351; 364; 378; 396; 407; 429; 444; 462; 468; 481; 518; 546; 567; 572; 594; 666; 693; 702; 756; 777; 814; 819; 858; 891; 924; 962; 999; 1,001; 1,036; 1,053; 1,092; 1,134; 1,188; 1,221; 1,287; 1,332; 1,386; 1,404; 1,443; 1,554; 1,628; 1,638; 1,716; 1,782; 1,924; 1,998; 2,002; 2,079; 2,106; 2,268; 2,331; 2,442; 2,457; 2,574; 2,772; 2,849; 2,886; 2,997; 3,003; 3,108; 3,276; 3,367; 3,564; 3,663; 3,861; 3,996; 4,004; 4,158; 4,212; 4,329; 4,662; 4,884; 4,914; 5,148; 5,291; 5,698; 5,772; 5,994; 6,006; 6,237; 6,734; 6,993; 7,326; 7,371; 7,722; 8,316; 8,547; 8,658; 9,009; 9,324; 9,828; 10,101; 10,582; 10,989; 11,396; 11,583; 11,988; 12,012; 12,474; 12,987; 13,468; 13,986; 14,652; 14,742; 15,444; 15,873; 17,094; 17,316; 18,018; 20,202; 20,979; 21,164; 21,978; 23,166; 24,948; 25,641; 25,974; 27,027; 27,972; 29,484; 30,303; 31,746; 32,967; 34,188; 36,036; 37,037; 38,961; 40,404; 41,958; 43,956; 46,332; 47,619; 51,282; 51,948; 54,054; 60,606; 63,492; 65,934; 74,074; 76,923; 77,922; 81,081; 83,916; 90,909; 95,238; 102,564; 108,108; 111,111; 121,212; 131,868; 142,857; 148,148; 153,846; 155,844; 162,162; 181,818; 190,476; 222,222; 230,769; 272,727; 285,714; 307,692; 324,324; 333,333; 363,636; 428,571; 444,444; 461,538; 545,454; 571,428; 666,666; 857,142; 923,076; 999,999; 1,090,908; 1,333,332; 1,714,284; 1,999,998; 2,999,997; 3,999,996; 5,999,994 and 11,999,988
out of which 6 prime factors: 2; 3; 7; 11; 13 and 37
11,999,988 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.


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".