Given the Number 472,056,816, Calculate (Find) All the Factors (All the Divisors) of the Number 472,056,816 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 472,056,816

1. Carry out the prime factorization of the number 472,056,816:

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


472,056,816 = 24 × 3 × 7 × 112 × 17 × 683
472,056,816 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 472,056,816

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
prime factor = 11
22 × 3 = 12
2 × 7 = 14
24 = 16
prime factor = 17
3 × 7 = 21
2 × 11 = 22
23 × 3 = 24
22 × 7 = 28
3 × 11 = 33
2 × 17 = 34
2 × 3 × 7 = 42
22 × 11 = 44
24 × 3 = 48
3 × 17 = 51
23 × 7 = 56
2 × 3 × 11 = 66
22 × 17 = 68
7 × 11 = 77
22 × 3 × 7 = 84
23 × 11 = 88
2 × 3 × 17 = 102
24 × 7 = 112
7 × 17 = 119
112 = 121
22 × 3 × 11 = 132
23 × 17 = 136
2 × 7 × 11 = 154
23 × 3 × 7 = 168
24 × 11 = 176
11 × 17 = 187
22 × 3 × 17 = 204
3 × 7 × 11 = 231
2 × 7 × 17 = 238
2 × 112 = 242
23 × 3 × 11 = 264
24 × 17 = 272
22 × 7 × 11 = 308
24 × 3 × 7 = 336
3 × 7 × 17 = 357
3 × 112 = 363
2 × 11 × 17 = 374
23 × 3 × 17 = 408
2 × 3 × 7 × 11 = 462
22 × 7 × 17 = 476
22 × 112 = 484
24 × 3 × 11 = 528
3 × 11 × 17 = 561
23 × 7 × 11 = 616
prime factor = 683
2 × 3 × 7 × 17 = 714
2 × 3 × 112 = 726
22 × 11 × 17 = 748
24 × 3 × 17 = 816
7 × 112 = 847
22 × 3 × 7 × 11 = 924
23 × 7 × 17 = 952
23 × 112 = 968
2 × 3 × 11 × 17 = 1,122
24 × 7 × 11 = 1,232
7 × 11 × 17 = 1,309
2 × 683 = 1,366
22 × 3 × 7 × 17 = 1,428
22 × 3 × 112 = 1,452
23 × 11 × 17 = 1,496
2 × 7 × 112 = 1,694
23 × 3 × 7 × 11 = 1,848
24 × 7 × 17 = 1,904
24 × 112 = 1,936
3 × 683 = 2,049
112 × 17 = 2,057
22 × 3 × 11 × 17 = 2,244
3 × 7 × 112 = 2,541
2 × 7 × 11 × 17 = 2,618
22 × 683 = 2,732
23 × 3 × 7 × 17 = 2,856
23 × 3 × 112 = 2,904
24 × 11 × 17 = 2,992
22 × 7 × 112 = 3,388
24 × 3 × 7 × 11 = 3,696
3 × 7 × 11 × 17 = 3,927
2 × 3 × 683 = 4,098
2 × 112 × 17 = 4,114
23 × 3 × 11 × 17 = 4,488
7 × 683 = 4,781
2 × 3 × 7 × 112 = 5,082
22 × 7 × 11 × 17 = 5,236
23 × 683 = 5,464
24 × 3 × 7 × 17 = 5,712
24 × 3 × 112 = 5,808
3 × 112 × 17 = 6,171
23 × 7 × 112 = 6,776
11 × 683 = 7,513
2 × 3 × 7 × 11 × 17 = 7,854
22 × 3 × 683 = 8,196
22 × 112 × 17 = 8,228
24 × 3 × 11 × 17 = 8,976
2 × 7 × 683 = 9,562
22 × 3 × 7 × 112 = 10,164
23 × 7 × 11 × 17 = 10,472
24 × 683 = 10,928
17 × 683 = 11,611
2 × 3 × 112 × 17 = 12,342
24 × 7 × 112 = 13,552
3 × 7 × 683 = 14,343
7 × 112 × 17 = 14,399
2 × 11 × 683 = 15,026
22 × 3 × 7 × 11 × 17 = 15,708
23 × 3 × 683 = 16,392
23 × 112 × 17 = 16,456
22 × 7 × 683 = 19,124
23 × 3 × 7 × 112 = 20,328
24 × 7 × 11 × 17 = 20,944
This list continues below...

... This list continues from above
3 × 11 × 683 = 22,539
2 × 17 × 683 = 23,222
22 × 3 × 112 × 17 = 24,684
2 × 3 × 7 × 683 = 28,686
2 × 7 × 112 × 17 = 28,798
22 × 11 × 683 = 30,052
23 × 3 × 7 × 11 × 17 = 31,416
24 × 3 × 683 = 32,784
24 × 112 × 17 = 32,912
3 × 17 × 683 = 34,833
23 × 7 × 683 = 38,248
24 × 3 × 7 × 112 = 40,656
3 × 7 × 112 × 17 = 43,197
2 × 3 × 11 × 683 = 45,078
22 × 17 × 683 = 46,444
23 × 3 × 112 × 17 = 49,368
7 × 11 × 683 = 52,591
22 × 3 × 7 × 683 = 57,372
22 × 7 × 112 × 17 = 57,596
23 × 11 × 683 = 60,104
24 × 3 × 7 × 11 × 17 = 62,832
2 × 3 × 17 × 683 = 69,666
24 × 7 × 683 = 76,496
7 × 17 × 683 = 81,277
112 × 683 = 82,643
2 × 3 × 7 × 112 × 17 = 86,394
22 × 3 × 11 × 683 = 90,156
23 × 17 × 683 = 92,888
24 × 3 × 112 × 17 = 98,736
2 × 7 × 11 × 683 = 105,182
23 × 3 × 7 × 683 = 114,744
23 × 7 × 112 × 17 = 115,192
24 × 11 × 683 = 120,208
11 × 17 × 683 = 127,721
22 × 3 × 17 × 683 = 139,332
3 × 7 × 11 × 683 = 157,773
2 × 7 × 17 × 683 = 162,554
2 × 112 × 683 = 165,286
22 × 3 × 7 × 112 × 17 = 172,788
23 × 3 × 11 × 683 = 180,312
24 × 17 × 683 = 185,776
22 × 7 × 11 × 683 = 210,364
24 × 3 × 7 × 683 = 229,488
24 × 7 × 112 × 17 = 230,384
3 × 7 × 17 × 683 = 243,831
3 × 112 × 683 = 247,929
2 × 11 × 17 × 683 = 255,442
23 × 3 × 17 × 683 = 278,664
2 × 3 × 7 × 11 × 683 = 315,546
22 × 7 × 17 × 683 = 325,108
22 × 112 × 683 = 330,572
23 × 3 × 7 × 112 × 17 = 345,576
24 × 3 × 11 × 683 = 360,624
3 × 11 × 17 × 683 = 383,163
23 × 7 × 11 × 683 = 420,728
2 × 3 × 7 × 17 × 683 = 487,662
2 × 3 × 112 × 683 = 495,858
22 × 11 × 17 × 683 = 510,884
24 × 3 × 17 × 683 = 557,328
7 × 112 × 683 = 578,501
22 × 3 × 7 × 11 × 683 = 631,092
23 × 7 × 17 × 683 = 650,216
23 × 112 × 683 = 661,144
24 × 3 × 7 × 112 × 17 = 691,152
2 × 3 × 11 × 17 × 683 = 766,326
24 × 7 × 11 × 683 = 841,456
7 × 11 × 17 × 683 = 894,047
22 × 3 × 7 × 17 × 683 = 975,324
22 × 3 × 112 × 683 = 991,716
23 × 11 × 17 × 683 = 1,021,768
2 × 7 × 112 × 683 = 1,157,002
23 × 3 × 7 × 11 × 683 = 1,262,184
24 × 7 × 17 × 683 = 1,300,432
24 × 112 × 683 = 1,322,288
112 × 17 × 683 = 1,404,931
22 × 3 × 11 × 17 × 683 = 1,532,652
3 × 7 × 112 × 683 = 1,735,503
2 × 7 × 11 × 17 × 683 = 1,788,094
23 × 3 × 7 × 17 × 683 = 1,950,648
23 × 3 × 112 × 683 = 1,983,432
24 × 11 × 17 × 683 = 2,043,536
22 × 7 × 112 × 683 = 2,314,004
24 × 3 × 7 × 11 × 683 = 2,524,368
3 × 7 × 11 × 17 × 683 = 2,682,141
2 × 112 × 17 × 683 = 2,809,862
23 × 3 × 11 × 17 × 683 = 3,065,304
2 × 3 × 7 × 112 × 683 = 3,471,006
22 × 7 × 11 × 17 × 683 = 3,576,188
24 × 3 × 7 × 17 × 683 = 3,901,296
24 × 3 × 112 × 683 = 3,966,864
3 × 112 × 17 × 683 = 4,214,793
23 × 7 × 112 × 683 = 4,628,008
2 × 3 × 7 × 11 × 17 × 683 = 5,364,282
22 × 112 × 17 × 683 = 5,619,724
24 × 3 × 11 × 17 × 683 = 6,130,608
22 × 3 × 7 × 112 × 683 = 6,942,012
23 × 7 × 11 × 17 × 683 = 7,152,376
2 × 3 × 112 × 17 × 683 = 8,429,586
24 × 7 × 112 × 683 = 9,256,016
7 × 112 × 17 × 683 = 9,834,517
22 × 3 × 7 × 11 × 17 × 683 = 10,728,564
23 × 112 × 17 × 683 = 11,239,448
23 × 3 × 7 × 112 × 683 = 13,884,024
24 × 7 × 11 × 17 × 683 = 14,304,752
22 × 3 × 112 × 17 × 683 = 16,859,172
2 × 7 × 112 × 17 × 683 = 19,669,034
23 × 3 × 7 × 11 × 17 × 683 = 21,457,128
24 × 112 × 17 × 683 = 22,478,896
24 × 3 × 7 × 112 × 683 = 27,768,048
3 × 7 × 112 × 17 × 683 = 29,503,551
23 × 3 × 112 × 17 × 683 = 33,718,344
22 × 7 × 112 × 17 × 683 = 39,338,068
24 × 3 × 7 × 11 × 17 × 683 = 42,914,256
2 × 3 × 7 × 112 × 17 × 683 = 59,007,102
24 × 3 × 112 × 17 × 683 = 67,436,688
23 × 7 × 112 × 17 × 683 = 78,676,136
22 × 3 × 7 × 112 × 17 × 683 = 118,014,204
24 × 7 × 112 × 17 × 683 = 157,352,272
23 × 3 × 7 × 112 × 17 × 683 = 236,028,408
24 × 3 × 7 × 112 × 17 × 683 = 472,056,816

The final answer:
(scroll down)

472,056,816 has 240 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 11; 12; 14; 16; 17; 21; 22; 24; 28; 33; 34; 42; 44; 48; 51; 56; 66; 68; 77; 84; 88; 102; 112; 119; 121; 132; 136; 154; 168; 176; 187; 204; 231; 238; 242; 264; 272; 308; 336; 357; 363; 374; 408; 462; 476; 484; 528; 561; 616; 683; 714; 726; 748; 816; 847; 924; 952; 968; 1,122; 1,232; 1,309; 1,366; 1,428; 1,452; 1,496; 1,694; 1,848; 1,904; 1,936; 2,049; 2,057; 2,244; 2,541; 2,618; 2,732; 2,856; 2,904; 2,992; 3,388; 3,696; 3,927; 4,098; 4,114; 4,488; 4,781; 5,082; 5,236; 5,464; 5,712; 5,808; 6,171; 6,776; 7,513; 7,854; 8,196; 8,228; 8,976; 9,562; 10,164; 10,472; 10,928; 11,611; 12,342; 13,552; 14,343; 14,399; 15,026; 15,708; 16,392; 16,456; 19,124; 20,328; 20,944; 22,539; 23,222; 24,684; 28,686; 28,798; 30,052; 31,416; 32,784; 32,912; 34,833; 38,248; 40,656; 43,197; 45,078; 46,444; 49,368; 52,591; 57,372; 57,596; 60,104; 62,832; 69,666; 76,496; 81,277; 82,643; 86,394; 90,156; 92,888; 98,736; 105,182; 114,744; 115,192; 120,208; 127,721; 139,332; 157,773; 162,554; 165,286; 172,788; 180,312; 185,776; 210,364; 229,488; 230,384; 243,831; 247,929; 255,442; 278,664; 315,546; 325,108; 330,572; 345,576; 360,624; 383,163; 420,728; 487,662; 495,858; 510,884; 557,328; 578,501; 631,092; 650,216; 661,144; 691,152; 766,326; 841,456; 894,047; 975,324; 991,716; 1,021,768; 1,157,002; 1,262,184; 1,300,432; 1,322,288; 1,404,931; 1,532,652; 1,735,503; 1,788,094; 1,950,648; 1,983,432; 2,043,536; 2,314,004; 2,524,368; 2,682,141; 2,809,862; 3,065,304; 3,471,006; 3,576,188; 3,901,296; 3,966,864; 4,214,793; 4,628,008; 5,364,282; 5,619,724; 6,130,608; 6,942,012; 7,152,376; 8,429,586; 9,256,016; 9,834,517; 10,728,564; 11,239,448; 13,884,024; 14,304,752; 16,859,172; 19,669,034; 21,457,128; 22,478,896; 27,768,048; 29,503,551; 33,718,344; 39,338,068; 42,914,256; 59,007,102; 67,436,688; 78,676,136; 118,014,204; 157,352,272; 236,028,408 and 472,056,816
out of which 6 prime factors: 2; 3; 7; 11; 17 and 683
472,056,816 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.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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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".