Given the Number 9,818,172 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 9,818,172

1. Carry out the prime factorization of the number 9,818,172:

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


9,818,172 = 22 × 36 × 7 × 13 × 37
9,818,172 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 9,818,172

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
prime factor = 13
2 × 7 = 14
2 × 32 = 18
3 × 7 = 21
2 × 13 = 26
33 = 27
22 × 7 = 28
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
22 × 13 = 52
2 × 33 = 54
32 × 7 = 63
2 × 37 = 74
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
7 × 13 = 91
22 × 33 = 108
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
22 × 37 = 148
22 × 3 × 13 = 156
2 × 34 = 162
2 × 7 × 13 = 182
33 × 7 = 189
2 × 3 × 37 = 222
2 × 32 × 13 = 234
35 = 243
22 × 32 × 7 = 252
7 × 37 = 259
3 × 7 × 13 = 273
22 × 34 = 324
32 × 37 = 333
33 × 13 = 351
22 × 7 × 13 = 364
2 × 33 × 7 = 378
22 × 3 × 37 = 444
22 × 32 × 13 = 468
13 × 37 = 481
2 × 35 = 486
2 × 7 × 37 = 518
2 × 3 × 7 × 13 = 546
34 × 7 = 567
2 × 32 × 37 = 666
2 × 33 × 13 = 702
36 = 729
22 × 33 × 7 = 756
3 × 7 × 37 = 777
32 × 7 × 13 = 819
2 × 13 × 37 = 962
22 × 35 = 972
33 × 37 = 999
22 × 7 × 37 = 1,036
34 × 13 = 1,053
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
22 × 32 × 37 = 1,332
22 × 33 × 13 = 1,404
3 × 13 × 37 = 1,443
2 × 36 = 1,458
2 × 3 × 7 × 37 = 1,554
2 × 32 × 7 × 13 = 1,638
35 × 7 = 1,701
22 × 13 × 37 = 1,924
2 × 33 × 37 = 1,998
2 × 34 × 13 = 2,106
22 × 34 × 7 = 2,268
32 × 7 × 37 = 2,331
33 × 7 × 13 = 2,457
2 × 3 × 13 × 37 = 2,886
22 × 36 = 2,916
34 × 37 = 2,997
22 × 3 × 7 × 37 = 3,108
This list continues below...

... This list continues from above
35 × 13 = 3,159
22 × 32 × 7 × 13 = 3,276
7 × 13 × 37 = 3,367
2 × 35 × 7 = 3,402
22 × 33 × 37 = 3,996
22 × 34 × 13 = 4,212
32 × 13 × 37 = 4,329
2 × 32 × 7 × 37 = 4,662
2 × 33 × 7 × 13 = 4,914
36 × 7 = 5,103
22 × 3 × 13 × 37 = 5,772
2 × 34 × 37 = 5,994
2 × 35 × 13 = 6,318
2 × 7 × 13 × 37 = 6,734
22 × 35 × 7 = 6,804
33 × 7 × 37 = 6,993
34 × 7 × 13 = 7,371
2 × 32 × 13 × 37 = 8,658
35 × 37 = 8,991
22 × 32 × 7 × 37 = 9,324
36 × 13 = 9,477
22 × 33 × 7 × 13 = 9,828
3 × 7 × 13 × 37 = 10,101
2 × 36 × 7 = 10,206
22 × 34 × 37 = 11,988
22 × 35 × 13 = 12,636
33 × 13 × 37 = 12,987
22 × 7 × 13 × 37 = 13,468
2 × 33 × 7 × 37 = 13,986
2 × 34 × 7 × 13 = 14,742
22 × 32 × 13 × 37 = 17,316
2 × 35 × 37 = 17,982
2 × 36 × 13 = 18,954
2 × 3 × 7 × 13 × 37 = 20,202
22 × 36 × 7 = 20,412
34 × 7 × 37 = 20,979
35 × 7 × 13 = 22,113
2 × 33 × 13 × 37 = 25,974
36 × 37 = 26,973
22 × 33 × 7 × 37 = 27,972
22 × 34 × 7 × 13 = 29,484
32 × 7 × 13 × 37 = 30,303
22 × 35 × 37 = 35,964
22 × 36 × 13 = 37,908
34 × 13 × 37 = 38,961
22 × 3 × 7 × 13 × 37 = 40,404
2 × 34 × 7 × 37 = 41,958
2 × 35 × 7 × 13 = 44,226
22 × 33 × 13 × 37 = 51,948
2 × 36 × 37 = 53,946
2 × 32 × 7 × 13 × 37 = 60,606
35 × 7 × 37 = 62,937
36 × 7 × 13 = 66,339
2 × 34 × 13 × 37 = 77,922
22 × 34 × 7 × 37 = 83,916
22 × 35 × 7 × 13 = 88,452
33 × 7 × 13 × 37 = 90,909
22 × 36 × 37 = 107,892
35 × 13 × 37 = 116,883
22 × 32 × 7 × 13 × 37 = 121,212
2 × 35 × 7 × 37 = 125,874
2 × 36 × 7 × 13 = 132,678
22 × 34 × 13 × 37 = 155,844
2 × 33 × 7 × 13 × 37 = 181,818
36 × 7 × 37 = 188,811
2 × 35 × 13 × 37 = 233,766
22 × 35 × 7 × 37 = 251,748
22 × 36 × 7 × 13 = 265,356
34 × 7 × 13 × 37 = 272,727
36 × 13 × 37 = 350,649
22 × 33 × 7 × 13 × 37 = 363,636
2 × 36 × 7 × 37 = 377,622
22 × 35 × 13 × 37 = 467,532
2 × 34 × 7 × 13 × 37 = 545,454
2 × 36 × 13 × 37 = 701,298
22 × 36 × 7 × 37 = 755,244
35 × 7 × 13 × 37 = 818,181
22 × 34 × 7 × 13 × 37 = 1,090,908
22 × 36 × 13 × 37 = 1,402,596
2 × 35 × 7 × 13 × 37 = 1,636,362
36 × 7 × 13 × 37 = 2,454,543
22 × 35 × 7 × 13 × 37 = 3,272,724
2 × 36 × 7 × 13 × 37 = 4,909,086
22 × 36 × 7 × 13 × 37 = 9,818,172

The final answer:
(scroll down)

9,818,172 has 168 factors (divisors):
1; 2; 3; 4; 6; 7; 9; 12; 13; 14; 18; 21; 26; 27; 28; 36; 37; 39; 42; 52; 54; 63; 74; 78; 81; 84; 91; 108; 111; 117; 126; 148; 156; 162; 182; 189; 222; 234; 243; 252; 259; 273; 324; 333; 351; 364; 378; 444; 468; 481; 486; 518; 546; 567; 666; 702; 729; 756; 777; 819; 962; 972; 999; 1,036; 1,053; 1,092; 1,134; 1,332; 1,404; 1,443; 1,458; 1,554; 1,638; 1,701; 1,924; 1,998; 2,106; 2,268; 2,331; 2,457; 2,886; 2,916; 2,997; 3,108; 3,159; 3,276; 3,367; 3,402; 3,996; 4,212; 4,329; 4,662; 4,914; 5,103; 5,772; 5,994; 6,318; 6,734; 6,804; 6,993; 7,371; 8,658; 8,991; 9,324; 9,477; 9,828; 10,101; 10,206; 11,988; 12,636; 12,987; 13,468; 13,986; 14,742; 17,316; 17,982; 18,954; 20,202; 20,412; 20,979; 22,113; 25,974; 26,973; 27,972; 29,484; 30,303; 35,964; 37,908; 38,961; 40,404; 41,958; 44,226; 51,948; 53,946; 60,606; 62,937; 66,339; 77,922; 83,916; 88,452; 90,909; 107,892; 116,883; 121,212; 125,874; 132,678; 155,844; 181,818; 188,811; 233,766; 251,748; 265,356; 272,727; 350,649; 363,636; 377,622; 467,532; 545,454; 701,298; 755,244; 818,181; 1,090,908; 1,402,596; 1,636,362; 2,454,543; 3,272,724; 4,909,086 and 9,818,172
out of which 5 prime factors: 2; 3; 7; 13 and 37
9,818,172 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".