Given the Number 48,426,336, Calculate (Find) All the Factors (All the Divisors) of the Number 48,426,336 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 48,426,336

1. Carry out the prime factorization of the number 48,426,336:

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


48,426,336 = 25 × 34 × 7 × 17 × 157
48,426,336 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 48,426,336

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
23 = 8
32 = 9
22 × 3 = 12
2 × 7 = 14
24 = 16
prime factor = 17
2 × 32 = 18
3 × 7 = 21
23 × 3 = 24
33 = 27
22 × 7 = 28
25 = 32
2 × 17 = 34
22 × 32 = 36
2 × 3 × 7 = 42
24 × 3 = 48
3 × 17 = 51
2 × 33 = 54
23 × 7 = 56
32 × 7 = 63
22 × 17 = 68
23 × 32 = 72
34 = 81
22 × 3 × 7 = 84
25 × 3 = 96
2 × 3 × 17 = 102
22 × 33 = 108
24 × 7 = 112
7 × 17 = 119
2 × 32 × 7 = 126
23 × 17 = 136
24 × 32 = 144
32 × 17 = 153
prime factor = 157
2 × 34 = 162
23 × 3 × 7 = 168
33 × 7 = 189
22 × 3 × 17 = 204
23 × 33 = 216
25 × 7 = 224
2 × 7 × 17 = 238
22 × 32 × 7 = 252
24 × 17 = 272
25 × 32 = 288
2 × 32 × 17 = 306
2 × 157 = 314
22 × 34 = 324
24 × 3 × 7 = 336
3 × 7 × 17 = 357
2 × 33 × 7 = 378
23 × 3 × 17 = 408
24 × 33 = 432
33 × 17 = 459
3 × 157 = 471
22 × 7 × 17 = 476
23 × 32 × 7 = 504
25 × 17 = 544
34 × 7 = 567
22 × 32 × 17 = 612
22 × 157 = 628
23 × 34 = 648
25 × 3 × 7 = 672
2 × 3 × 7 × 17 = 714
22 × 33 × 7 = 756
24 × 3 × 17 = 816
25 × 33 = 864
2 × 33 × 17 = 918
2 × 3 × 157 = 942
23 × 7 × 17 = 952
24 × 32 × 7 = 1,008
32 × 7 × 17 = 1,071
7 × 157 = 1,099
2 × 34 × 7 = 1,134
23 × 32 × 17 = 1,224
23 × 157 = 1,256
24 × 34 = 1,296
34 × 17 = 1,377
32 × 157 = 1,413
22 × 3 × 7 × 17 = 1,428
23 × 33 × 7 = 1,512
25 × 3 × 17 = 1,632
22 × 33 × 17 = 1,836
22 × 3 × 157 = 1,884
24 × 7 × 17 = 1,904
25 × 32 × 7 = 2,016
2 × 32 × 7 × 17 = 2,142
2 × 7 × 157 = 2,198
22 × 34 × 7 = 2,268
24 × 32 × 17 = 2,448
24 × 157 = 2,512
25 × 34 = 2,592
17 × 157 = 2,669
2 × 34 × 17 = 2,754
2 × 32 × 157 = 2,826
23 × 3 × 7 × 17 = 2,856
24 × 33 × 7 = 3,024
33 × 7 × 17 = 3,213
3 × 7 × 157 = 3,297
23 × 33 × 17 = 3,672
23 × 3 × 157 = 3,768
25 × 7 × 17 = 3,808
33 × 157 = 4,239
22 × 32 × 7 × 17 = 4,284
22 × 7 × 157 = 4,396
23 × 34 × 7 = 4,536
25 × 32 × 17 = 4,896
25 × 157 = 5,024
2 × 17 × 157 = 5,338
22 × 34 × 17 = 5,508
22 × 32 × 157 = 5,652
24 × 3 × 7 × 17 = 5,712
25 × 33 × 7 = 6,048
2 × 33 × 7 × 17 = 6,426
2 × 3 × 7 × 157 = 6,594
This list continues below...

... This list continues from above
24 × 33 × 17 = 7,344
24 × 3 × 157 = 7,536
3 × 17 × 157 = 8,007
2 × 33 × 157 = 8,478
23 × 32 × 7 × 17 = 8,568
23 × 7 × 157 = 8,792
24 × 34 × 7 = 9,072
34 × 7 × 17 = 9,639
32 × 7 × 157 = 9,891
22 × 17 × 157 = 10,676
23 × 34 × 17 = 11,016
23 × 32 × 157 = 11,304
25 × 3 × 7 × 17 = 11,424
34 × 157 = 12,717
22 × 33 × 7 × 17 = 12,852
22 × 3 × 7 × 157 = 13,188
25 × 33 × 17 = 14,688
25 × 3 × 157 = 15,072
2 × 3 × 17 × 157 = 16,014
22 × 33 × 157 = 16,956
24 × 32 × 7 × 17 = 17,136
24 × 7 × 157 = 17,584
25 × 34 × 7 = 18,144
7 × 17 × 157 = 18,683
2 × 34 × 7 × 17 = 19,278
2 × 32 × 7 × 157 = 19,782
23 × 17 × 157 = 21,352
24 × 34 × 17 = 22,032
24 × 32 × 157 = 22,608
32 × 17 × 157 = 24,021
2 × 34 × 157 = 25,434
23 × 33 × 7 × 17 = 25,704
23 × 3 × 7 × 157 = 26,376
33 × 7 × 157 = 29,673
22 × 3 × 17 × 157 = 32,028
23 × 33 × 157 = 33,912
25 × 32 × 7 × 17 = 34,272
25 × 7 × 157 = 35,168
2 × 7 × 17 × 157 = 37,366
22 × 34 × 7 × 17 = 38,556
22 × 32 × 7 × 157 = 39,564
24 × 17 × 157 = 42,704
25 × 34 × 17 = 44,064
25 × 32 × 157 = 45,216
2 × 32 × 17 × 157 = 48,042
22 × 34 × 157 = 50,868
24 × 33 × 7 × 17 = 51,408
24 × 3 × 7 × 157 = 52,752
3 × 7 × 17 × 157 = 56,049
2 × 33 × 7 × 157 = 59,346
23 × 3 × 17 × 157 = 64,056
24 × 33 × 157 = 67,824
33 × 17 × 157 = 72,063
22 × 7 × 17 × 157 = 74,732
23 × 34 × 7 × 17 = 77,112
23 × 32 × 7 × 157 = 79,128
25 × 17 × 157 = 85,408
34 × 7 × 157 = 89,019
22 × 32 × 17 × 157 = 96,084
23 × 34 × 157 = 101,736
25 × 33 × 7 × 17 = 102,816
25 × 3 × 7 × 157 = 105,504
2 × 3 × 7 × 17 × 157 = 112,098
22 × 33 × 7 × 157 = 118,692
24 × 3 × 17 × 157 = 128,112
25 × 33 × 157 = 135,648
2 × 33 × 17 × 157 = 144,126
23 × 7 × 17 × 157 = 149,464
24 × 34 × 7 × 17 = 154,224
24 × 32 × 7 × 157 = 158,256
32 × 7 × 17 × 157 = 168,147
2 × 34 × 7 × 157 = 178,038
23 × 32 × 17 × 157 = 192,168
24 × 34 × 157 = 203,472
34 × 17 × 157 = 216,189
22 × 3 × 7 × 17 × 157 = 224,196
23 × 33 × 7 × 157 = 237,384
25 × 3 × 17 × 157 = 256,224
22 × 33 × 17 × 157 = 288,252
24 × 7 × 17 × 157 = 298,928
25 × 34 × 7 × 17 = 308,448
25 × 32 × 7 × 157 = 316,512
2 × 32 × 7 × 17 × 157 = 336,294
22 × 34 × 7 × 157 = 356,076
24 × 32 × 17 × 157 = 384,336
25 × 34 × 157 = 406,944
2 × 34 × 17 × 157 = 432,378
23 × 3 × 7 × 17 × 157 = 448,392
24 × 33 × 7 × 157 = 474,768
33 × 7 × 17 × 157 = 504,441
23 × 33 × 17 × 157 = 576,504
25 × 7 × 17 × 157 = 597,856
22 × 32 × 7 × 17 × 157 = 672,588
23 × 34 × 7 × 157 = 712,152
25 × 32 × 17 × 157 = 768,672
22 × 34 × 17 × 157 = 864,756
24 × 3 × 7 × 17 × 157 = 896,784
25 × 33 × 7 × 157 = 949,536
2 × 33 × 7 × 17 × 157 = 1,008,882
24 × 33 × 17 × 157 = 1,153,008
23 × 32 × 7 × 17 × 157 = 1,345,176
24 × 34 × 7 × 157 = 1,424,304
34 × 7 × 17 × 157 = 1,513,323
23 × 34 × 17 × 157 = 1,729,512
25 × 3 × 7 × 17 × 157 = 1,793,568
22 × 33 × 7 × 17 × 157 = 2,017,764
25 × 33 × 17 × 157 = 2,306,016
24 × 32 × 7 × 17 × 157 = 2,690,352
25 × 34 × 7 × 157 = 2,848,608
2 × 34 × 7 × 17 × 157 = 3,026,646
24 × 34 × 17 × 157 = 3,459,024
23 × 33 × 7 × 17 × 157 = 4,035,528
25 × 32 × 7 × 17 × 157 = 5,380,704
22 × 34 × 7 × 17 × 157 = 6,053,292
25 × 34 × 17 × 157 = 6,918,048
24 × 33 × 7 × 17 × 157 = 8,071,056
23 × 34 × 7 × 17 × 157 = 12,106,584
25 × 33 × 7 × 17 × 157 = 16,142,112
24 × 34 × 7 × 17 × 157 = 24,213,168
25 × 34 × 7 × 17 × 157 = 48,426,336

The final answer:
(scroll down)

48,426,336 has 240 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 12; 14; 16; 17; 18; 21; 24; 27; 28; 32; 34; 36; 42; 48; 51; 54; 56; 63; 68; 72; 81; 84; 96; 102; 108; 112; 119; 126; 136; 144; 153; 157; 162; 168; 189; 204; 216; 224; 238; 252; 272; 288; 306; 314; 324; 336; 357; 378; 408; 432; 459; 471; 476; 504; 544; 567; 612; 628; 648; 672; 714; 756; 816; 864; 918; 942; 952; 1,008; 1,071; 1,099; 1,134; 1,224; 1,256; 1,296; 1,377; 1,413; 1,428; 1,512; 1,632; 1,836; 1,884; 1,904; 2,016; 2,142; 2,198; 2,268; 2,448; 2,512; 2,592; 2,669; 2,754; 2,826; 2,856; 3,024; 3,213; 3,297; 3,672; 3,768; 3,808; 4,239; 4,284; 4,396; 4,536; 4,896; 5,024; 5,338; 5,508; 5,652; 5,712; 6,048; 6,426; 6,594; 7,344; 7,536; 8,007; 8,478; 8,568; 8,792; 9,072; 9,639; 9,891; 10,676; 11,016; 11,304; 11,424; 12,717; 12,852; 13,188; 14,688; 15,072; 16,014; 16,956; 17,136; 17,584; 18,144; 18,683; 19,278; 19,782; 21,352; 22,032; 22,608; 24,021; 25,434; 25,704; 26,376; 29,673; 32,028; 33,912; 34,272; 35,168; 37,366; 38,556; 39,564; 42,704; 44,064; 45,216; 48,042; 50,868; 51,408; 52,752; 56,049; 59,346; 64,056; 67,824; 72,063; 74,732; 77,112; 79,128; 85,408; 89,019; 96,084; 101,736; 102,816; 105,504; 112,098; 118,692; 128,112; 135,648; 144,126; 149,464; 154,224; 158,256; 168,147; 178,038; 192,168; 203,472; 216,189; 224,196; 237,384; 256,224; 288,252; 298,928; 308,448; 316,512; 336,294; 356,076; 384,336; 406,944; 432,378; 448,392; 474,768; 504,441; 576,504; 597,856; 672,588; 712,152; 768,672; 864,756; 896,784; 949,536; 1,008,882; 1,153,008; 1,345,176; 1,424,304; 1,513,323; 1,729,512; 1,793,568; 2,017,764; 2,306,016; 2,690,352; 2,848,608; 3,026,646; 3,459,024; 4,035,528; 5,380,704; 6,053,292; 6,918,048; 8,071,056; 12,106,584; 16,142,112; 24,213,168 and 48,426,336
out of which 5 prime factors: 2; 3; 7; 17 and 157
48,426,336 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.

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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".