Given the Number 2,918,916 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 2,918,916

1. Carry out the prime factorization of the number 2,918,916:

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


2,918,916 = 22 × 36 × 7 × 11 × 13
2,918,916 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 2,918,916

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
3 × 13 = 39
2 × 3 × 7 = 42
22 × 11 = 44
22 × 13 = 52
2 × 33 = 54
32 × 7 = 63
2 × 3 × 11 = 66
7 × 11 = 77
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
7 × 13 = 91
32 × 11 = 99
22 × 33 = 108
32 × 13 = 117
2 × 32 × 7 = 126
22 × 3 × 11 = 132
11 × 13 = 143
2 × 7 × 11 = 154
22 × 3 × 13 = 156
2 × 34 = 162
2 × 7 × 13 = 182
33 × 7 = 189
2 × 32 × 11 = 198
3 × 7 × 11 = 231
2 × 32 × 13 = 234
35 = 243
22 × 32 × 7 = 252
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
22 × 7 × 11 = 308
22 × 34 = 324
33 × 13 = 351
22 × 7 × 13 = 364
2 × 33 × 7 = 378
22 × 32 × 11 = 396
3 × 11 × 13 = 429
2 × 3 × 7 × 11 = 462
22 × 32 × 13 = 468
2 × 35 = 486
2 × 3 × 7 × 13 = 546
34 × 7 = 567
22 × 11 × 13 = 572
2 × 33 × 11 = 594
32 × 7 × 11 = 693
2 × 33 × 13 = 702
36 = 729
22 × 33 × 7 = 756
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
34 × 11 = 891
22 × 3 × 7 × 11 = 924
22 × 35 = 972
7 × 11 × 13 = 1,001
34 × 13 = 1,053
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
22 × 33 × 11 = 1,188
32 × 11 × 13 = 1,287
2 × 32 × 7 × 11 = 1,386
22 × 33 × 13 = 1,404
2 × 36 = 1,458
2 × 32 × 7 × 13 = 1,638
35 × 7 = 1,701
This list continues below...

... This list continues from above
22 × 3 × 11 × 13 = 1,716
2 × 34 × 11 = 1,782
2 × 7 × 11 × 13 = 2,002
33 × 7 × 11 = 2,079
2 × 34 × 13 = 2,106
22 × 34 × 7 = 2,268
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
35 × 11 = 2,673
22 × 32 × 7 × 11 = 2,772
22 × 36 = 2,916
3 × 7 × 11 × 13 = 3,003
35 × 13 = 3,159
22 × 32 × 7 × 13 = 3,276
2 × 35 × 7 = 3,402
22 × 34 × 11 = 3,564
33 × 11 × 13 = 3,861
22 × 7 × 11 × 13 = 4,004
2 × 33 × 7 × 11 = 4,158
22 × 34 × 13 = 4,212
2 × 33 × 7 × 13 = 4,914
36 × 7 = 5,103
22 × 32 × 11 × 13 = 5,148
2 × 35 × 11 = 5,346
2 × 3 × 7 × 11 × 13 = 6,006
34 × 7 × 11 = 6,237
2 × 35 × 13 = 6,318
22 × 35 × 7 = 6,804
34 × 7 × 13 = 7,371
2 × 33 × 11 × 13 = 7,722
36 × 11 = 8,019
22 × 33 × 7 × 11 = 8,316
32 × 7 × 11 × 13 = 9,009
36 × 13 = 9,477
22 × 33 × 7 × 13 = 9,828
2 × 36 × 7 = 10,206
22 × 35 × 11 = 10,692
34 × 11 × 13 = 11,583
22 × 3 × 7 × 11 × 13 = 12,012
2 × 34 × 7 × 11 = 12,474
22 × 35 × 13 = 12,636
2 × 34 × 7 × 13 = 14,742
22 × 33 × 11 × 13 = 15,444
2 × 36 × 11 = 16,038
2 × 32 × 7 × 11 × 13 = 18,018
35 × 7 × 11 = 18,711
2 × 36 × 13 = 18,954
22 × 36 × 7 = 20,412
35 × 7 × 13 = 22,113
2 × 34 × 11 × 13 = 23,166
22 × 34 × 7 × 11 = 24,948
33 × 7 × 11 × 13 = 27,027
22 × 34 × 7 × 13 = 29,484
22 × 36 × 11 = 32,076
35 × 11 × 13 = 34,749
22 × 32 × 7 × 11 × 13 = 36,036
2 × 35 × 7 × 11 = 37,422
22 × 36 × 13 = 37,908
2 × 35 × 7 × 13 = 44,226
22 × 34 × 11 × 13 = 46,332
2 × 33 × 7 × 11 × 13 = 54,054
36 × 7 × 11 = 56,133
36 × 7 × 13 = 66,339
2 × 35 × 11 × 13 = 69,498
22 × 35 × 7 × 11 = 74,844
34 × 7 × 11 × 13 = 81,081
22 × 35 × 7 × 13 = 88,452
36 × 11 × 13 = 104,247
22 × 33 × 7 × 11 × 13 = 108,108
2 × 36 × 7 × 11 = 112,266
2 × 36 × 7 × 13 = 132,678
22 × 35 × 11 × 13 = 138,996
2 × 34 × 7 × 11 × 13 = 162,162
2 × 36 × 11 × 13 = 208,494
22 × 36 × 7 × 11 = 224,532
35 × 7 × 11 × 13 = 243,243
22 × 36 × 7 × 13 = 265,356
22 × 34 × 7 × 11 × 13 = 324,324
22 × 36 × 11 × 13 = 416,988
2 × 35 × 7 × 11 × 13 = 486,486
36 × 7 × 11 × 13 = 729,729
22 × 35 × 7 × 11 × 13 = 972,972
2 × 36 × 7 × 11 × 13 = 1,459,458
22 × 36 × 7 × 11 × 13 = 2,918,916

The final answer:
(scroll down)

2,918,916 has 168 factors (divisors):
1; 2; 3; 4; 6; 7; 9; 11; 12; 13; 14; 18; 21; 22; 26; 27; 28; 33; 36; 39; 42; 44; 52; 54; 63; 66; 77; 78; 81; 84; 91; 99; 108; 117; 126; 132; 143; 154; 156; 162; 182; 189; 198; 231; 234; 243; 252; 273; 286; 297; 308; 324; 351; 364; 378; 396; 429; 462; 468; 486; 546; 567; 572; 594; 693; 702; 729; 756; 819; 858; 891; 924; 972; 1,001; 1,053; 1,092; 1,134; 1,188; 1,287; 1,386; 1,404; 1,458; 1,638; 1,701; 1,716; 1,782; 2,002; 2,079; 2,106; 2,268; 2,457; 2,574; 2,673; 2,772; 2,916; 3,003; 3,159; 3,276; 3,402; 3,564; 3,861; 4,004; 4,158; 4,212; 4,914; 5,103; 5,148; 5,346; 6,006; 6,237; 6,318; 6,804; 7,371; 7,722; 8,019; 8,316; 9,009; 9,477; 9,828; 10,206; 10,692; 11,583; 12,012; 12,474; 12,636; 14,742; 15,444; 16,038; 18,018; 18,711; 18,954; 20,412; 22,113; 23,166; 24,948; 27,027; 29,484; 32,076; 34,749; 36,036; 37,422; 37,908; 44,226; 46,332; 54,054; 56,133; 66,339; 69,498; 74,844; 81,081; 88,452; 104,247; 108,108; 112,266; 132,678; 138,996; 162,162; 208,494; 224,532; 243,243; 265,356; 324,324; 416,988; 486,486; 729,729; 972,972; 1,459,458 and 2,918,916
out of which 5 prime factors: 2; 3; 7; 11 and 13
2,918,916 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".