Given the Number 15,428,556 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 15,428,556

1. Carry out the prime factorization of the number 15,428,556:

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


15,428,556 = 22 × 36 × 11 × 13 × 37
15,428,556 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 15,428,556

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
32 = 9
prime factor = 11
22 × 3 = 12
prime factor = 13
2 × 32 = 18
2 × 11 = 22
2 × 13 = 26
33 = 27
3 × 11 = 33
22 × 32 = 36
prime factor = 37
3 × 13 = 39
22 × 11 = 44
22 × 13 = 52
2 × 33 = 54
2 × 3 × 11 = 66
2 × 37 = 74
2 × 3 × 13 = 78
34 = 81
32 × 11 = 99
22 × 33 = 108
3 × 37 = 111
32 × 13 = 117
22 × 3 × 11 = 132
11 × 13 = 143
22 × 37 = 148
22 × 3 × 13 = 156
2 × 34 = 162
2 × 32 × 11 = 198
2 × 3 × 37 = 222
2 × 32 × 13 = 234
35 = 243
2 × 11 × 13 = 286
33 × 11 = 297
22 × 34 = 324
32 × 37 = 333
33 × 13 = 351
22 × 32 × 11 = 396
11 × 37 = 407
3 × 11 × 13 = 429
22 × 3 × 37 = 444
22 × 32 × 13 = 468
13 × 37 = 481
2 × 35 = 486
22 × 11 × 13 = 572
2 × 33 × 11 = 594
2 × 32 × 37 = 666
2 × 33 × 13 = 702
36 = 729
2 × 11 × 37 = 814
2 × 3 × 11 × 13 = 858
34 × 11 = 891
2 × 13 × 37 = 962
22 × 35 = 972
33 × 37 = 999
34 × 13 = 1,053
22 × 33 × 11 = 1,188
3 × 11 × 37 = 1,221
32 × 11 × 13 = 1,287
22 × 32 × 37 = 1,332
22 × 33 × 13 = 1,404
3 × 13 × 37 = 1,443
2 × 36 = 1,458
22 × 11 × 37 = 1,628
22 × 3 × 11 × 13 = 1,716
2 × 34 × 11 = 1,782
22 × 13 × 37 = 1,924
2 × 33 × 37 = 1,998
2 × 34 × 13 = 2,106
2 × 3 × 11 × 37 = 2,442
2 × 32 × 11 × 13 = 2,574
35 × 11 = 2,673
2 × 3 × 13 × 37 = 2,886
22 × 36 = 2,916
34 × 37 = 2,997
35 × 13 = 3,159
22 × 34 × 11 = 3,564
32 × 11 × 37 = 3,663
33 × 11 × 13 = 3,861
This list continues below...

... This list continues from above
22 × 33 × 37 = 3,996
22 × 34 × 13 = 4,212
32 × 13 × 37 = 4,329
22 × 3 × 11 × 37 = 4,884
22 × 32 × 11 × 13 = 5,148
11 × 13 × 37 = 5,291
2 × 35 × 11 = 5,346
22 × 3 × 13 × 37 = 5,772
2 × 34 × 37 = 5,994
2 × 35 × 13 = 6,318
2 × 32 × 11 × 37 = 7,326
2 × 33 × 11 × 13 = 7,722
36 × 11 = 8,019
2 × 32 × 13 × 37 = 8,658
35 × 37 = 8,991
36 × 13 = 9,477
2 × 11 × 13 × 37 = 10,582
22 × 35 × 11 = 10,692
33 × 11 × 37 = 10,989
34 × 11 × 13 = 11,583
22 × 34 × 37 = 11,988
22 × 35 × 13 = 12,636
33 × 13 × 37 = 12,987
22 × 32 × 11 × 37 = 14,652
22 × 33 × 11 × 13 = 15,444
3 × 11 × 13 × 37 = 15,873
2 × 36 × 11 = 16,038
22 × 32 × 13 × 37 = 17,316
2 × 35 × 37 = 17,982
2 × 36 × 13 = 18,954
22 × 11 × 13 × 37 = 21,164
2 × 33 × 11 × 37 = 21,978
2 × 34 × 11 × 13 = 23,166
2 × 33 × 13 × 37 = 25,974
36 × 37 = 26,973
2 × 3 × 11 × 13 × 37 = 31,746
22 × 36 × 11 = 32,076
34 × 11 × 37 = 32,967
35 × 11 × 13 = 34,749
22 × 35 × 37 = 35,964
22 × 36 × 13 = 37,908
34 × 13 × 37 = 38,961
22 × 33 × 11 × 37 = 43,956
22 × 34 × 11 × 13 = 46,332
32 × 11 × 13 × 37 = 47,619
22 × 33 × 13 × 37 = 51,948
2 × 36 × 37 = 53,946
22 × 3 × 11 × 13 × 37 = 63,492
2 × 34 × 11 × 37 = 65,934
2 × 35 × 11 × 13 = 69,498
2 × 34 × 13 × 37 = 77,922
2 × 32 × 11 × 13 × 37 = 95,238
35 × 11 × 37 = 98,901
36 × 11 × 13 = 104,247
22 × 36 × 37 = 107,892
35 × 13 × 37 = 116,883
22 × 34 × 11 × 37 = 131,868
22 × 35 × 11 × 13 = 138,996
33 × 11 × 13 × 37 = 142,857
22 × 34 × 13 × 37 = 155,844
22 × 32 × 11 × 13 × 37 = 190,476
2 × 35 × 11 × 37 = 197,802
2 × 36 × 11 × 13 = 208,494
2 × 35 × 13 × 37 = 233,766
2 × 33 × 11 × 13 × 37 = 285,714
36 × 11 × 37 = 296,703
36 × 13 × 37 = 350,649
22 × 35 × 11 × 37 = 395,604
22 × 36 × 11 × 13 = 416,988
34 × 11 × 13 × 37 = 428,571
22 × 35 × 13 × 37 = 467,532
22 × 33 × 11 × 13 × 37 = 571,428
2 × 36 × 11 × 37 = 593,406
2 × 36 × 13 × 37 = 701,298
2 × 34 × 11 × 13 × 37 = 857,142
22 × 36 × 11 × 37 = 1,186,812
35 × 11 × 13 × 37 = 1,285,713
22 × 36 × 13 × 37 = 1,402,596
22 × 34 × 11 × 13 × 37 = 1,714,284
2 × 35 × 11 × 13 × 37 = 2,571,426
36 × 11 × 13 × 37 = 3,857,139
22 × 35 × 11 × 13 × 37 = 5,142,852
2 × 36 × 11 × 13 × 37 = 7,714,278
22 × 36 × 11 × 13 × 37 = 15,428,556

The final answer:
(scroll down)

15,428,556 has 168 factors (divisors):
1; 2; 3; 4; 6; 9; 11; 12; 13; 18; 22; 26; 27; 33; 36; 37; 39; 44; 52; 54; 66; 74; 78; 81; 99; 108; 111; 117; 132; 143; 148; 156; 162; 198; 222; 234; 243; 286; 297; 324; 333; 351; 396; 407; 429; 444; 468; 481; 486; 572; 594; 666; 702; 729; 814; 858; 891; 962; 972; 999; 1,053; 1,188; 1,221; 1,287; 1,332; 1,404; 1,443; 1,458; 1,628; 1,716; 1,782; 1,924; 1,998; 2,106; 2,442; 2,574; 2,673; 2,886; 2,916; 2,997; 3,159; 3,564; 3,663; 3,861; 3,996; 4,212; 4,329; 4,884; 5,148; 5,291; 5,346; 5,772; 5,994; 6,318; 7,326; 7,722; 8,019; 8,658; 8,991; 9,477; 10,582; 10,692; 10,989; 11,583; 11,988; 12,636; 12,987; 14,652; 15,444; 15,873; 16,038; 17,316; 17,982; 18,954; 21,164; 21,978; 23,166; 25,974; 26,973; 31,746; 32,076; 32,967; 34,749; 35,964; 37,908; 38,961; 43,956; 46,332; 47,619; 51,948; 53,946; 63,492; 65,934; 69,498; 77,922; 95,238; 98,901; 104,247; 107,892; 116,883; 131,868; 138,996; 142,857; 155,844; 190,476; 197,802; 208,494; 233,766; 285,714; 296,703; 350,649; 395,604; 416,988; 428,571; 467,532; 571,428; 593,406; 701,298; 857,142; 1,186,812; 1,285,713; 1,402,596; 1,714,284; 2,571,426; 3,857,139; 5,142,852; 7,714,278 and 15,428,556
out of which 5 prime factors: 2; 3; 11; 13 and 37
15,428,556 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".