Given the Number 10,007,712, Calculate (Find) All the Factors (All the Divisors) of the Number 10,007,712 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 10,007,712

1. Carry out the prime factorization of the number 10,007,712:

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

10,007,712 = 25 × 37 × 11 × 13
10,007,712 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* 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 10,007,712

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
23 = 8
32 = 9
prime factor = 11
22 × 3 = 12
prime factor = 13
24 = 16
2 × 32 = 18
2 × 11 = 22
23 × 3 = 24
2 × 13 = 26
33 = 27
25 = 32
3 × 11 = 33
22 × 32 = 36
3 × 13 = 39
22 × 11 = 44
24 × 3 = 48
22 × 13 = 52
2 × 33 = 54
2 × 3 × 11 = 66
23 × 32 = 72
2 × 3 × 13 = 78
34 = 81
23 × 11 = 88
25 × 3 = 96
32 × 11 = 99
23 × 13 = 104
22 × 33 = 108
32 × 13 = 117
22 × 3 × 11 = 132
11 × 13 = 143
24 × 32 = 144
22 × 3 × 13 = 156
2 × 34 = 162
24 × 11 = 176
2 × 32 × 11 = 198
24 × 13 = 208
23 × 33 = 216
2 × 32 × 13 = 234
35 = 243
23 × 3 × 11 = 264
2 × 11 × 13 = 286
25 × 32 = 288
33 × 11 = 297
23 × 3 × 13 = 312
22 × 34 = 324
33 × 13 = 351
25 × 11 = 352
22 × 32 × 11 = 396
25 × 13 = 416
3 × 11 × 13 = 429
24 × 33 = 432
22 × 32 × 13 = 468
2 × 35 = 486
24 × 3 × 11 = 528
22 × 11 × 13 = 572
2 × 33 × 11 = 594
24 × 3 × 13 = 624
23 × 34 = 648
2 × 33 × 13 = 702
36 = 729
23 × 32 × 11 = 792
2 × 3 × 11 × 13 = 858
25 × 33 = 864
34 × 11 = 891
23 × 32 × 13 = 936
22 × 35 = 972
34 × 13 = 1,053
25 × 3 × 11 = 1,056
23 × 11 × 13 = 1,144
22 × 33 × 11 = 1,188
25 × 3 × 13 = 1,248
32 × 11 × 13 = 1,287
24 × 34 = 1,296
22 × 33 × 13 = 1,404
2 × 36 = 1,458
24 × 32 × 11 = 1,584
22 × 3 × 11 × 13 = 1,716
2 × 34 × 11 = 1,782
24 × 32 × 13 = 1,872
23 × 35 = 1,944
2 × 34 × 13 = 2,106
37 = 2,187
24 × 11 × 13 = 2,288
23 × 33 × 11 = 2,376
2 × 32 × 11 × 13 = 2,574
25 × 34 = 2,592
35 × 11 = 2,673
23 × 33 × 13 = 2,808
22 × 36 = 2,916
35 × 13 = 3,159
This list continues below...

... This list continues from above
25 × 32 × 11 = 3,168
23 × 3 × 11 × 13 = 3,432
22 × 34 × 11 = 3,564
25 × 32 × 13 = 3,744
33 × 11 × 13 = 3,861
24 × 35 = 3,888
22 × 34 × 13 = 4,212
2 × 37 = 4,374
25 × 11 × 13 = 4,576
24 × 33 × 11 = 4,752
22 × 32 × 11 × 13 = 5,148
2 × 35 × 11 = 5,346
24 × 33 × 13 = 5,616
23 × 36 = 5,832
2 × 35 × 13 = 6,318
24 × 3 × 11 × 13 = 6,864
23 × 34 × 11 = 7,128
2 × 33 × 11 × 13 = 7,722
25 × 35 = 7,776
36 × 11 = 8,019
23 × 34 × 13 = 8,424
22 × 37 = 8,748
36 × 13 = 9,477
25 × 33 × 11 = 9,504
23 × 32 × 11 × 13 = 10,296
22 × 35 × 11 = 10,692
25 × 33 × 13 = 11,232
34 × 11 × 13 = 11,583
24 × 36 = 11,664
22 × 35 × 13 = 12,636
25 × 3 × 11 × 13 = 13,728
24 × 34 × 11 = 14,256
22 × 33 × 11 × 13 = 15,444
2 × 36 × 11 = 16,038
24 × 34 × 13 = 16,848
23 × 37 = 17,496
2 × 36 × 13 = 18,954
24 × 32 × 11 × 13 = 20,592
23 × 35 × 11 = 21,384
2 × 34 × 11 × 13 = 23,166
25 × 36 = 23,328
37 × 11 = 24,057
23 × 35 × 13 = 25,272
37 × 13 = 28,431
25 × 34 × 11 = 28,512
23 × 33 × 11 × 13 = 30,888
22 × 36 × 11 = 32,076
25 × 34 × 13 = 33,696
35 × 11 × 13 = 34,749
24 × 37 = 34,992
22 × 36 × 13 = 37,908
25 × 32 × 11 × 13 = 41,184
24 × 35 × 11 = 42,768
22 × 34 × 11 × 13 = 46,332
2 × 37 × 11 = 48,114
24 × 35 × 13 = 50,544
2 × 37 × 13 = 56,862
24 × 33 × 11 × 13 = 61,776
23 × 36 × 11 = 64,152
2 × 35 × 11 × 13 = 69,498
25 × 37 = 69,984
23 × 36 × 13 = 75,816
25 × 35 × 11 = 85,536
23 × 34 × 11 × 13 = 92,664
22 × 37 × 11 = 96,228
25 × 35 × 13 = 101,088
36 × 11 × 13 = 104,247
22 × 37 × 13 = 113,724
25 × 33 × 11 × 13 = 123,552
24 × 36 × 11 = 128,304
22 × 35 × 11 × 13 = 138,996
24 × 36 × 13 = 151,632
24 × 34 × 11 × 13 = 185,328
23 × 37 × 11 = 192,456
2 × 36 × 11 × 13 = 208,494
23 × 37 × 13 = 227,448
25 × 36 × 11 = 256,608
23 × 35 × 11 × 13 = 277,992
25 × 36 × 13 = 303,264
37 × 11 × 13 = 312,741
25 × 34 × 11 × 13 = 370,656
24 × 37 × 11 = 384,912
22 × 36 × 11 × 13 = 416,988
24 × 37 × 13 = 454,896
24 × 35 × 11 × 13 = 555,984
2 × 37 × 11 × 13 = 625,482
25 × 37 × 11 = 769,824
23 × 36 × 11 × 13 = 833,976
25 × 37 × 13 = 909,792
25 × 35 × 11 × 13 = 1,111,968
22 × 37 × 11 × 13 = 1,250,964
24 × 36 × 11 × 13 = 1,667,952
23 × 37 × 11 × 13 = 2,501,928
25 × 36 × 11 × 13 = 3,335,904
24 × 37 × 11 × 13 = 5,003,856
25 × 37 × 11 × 13 = 10,007,712

The final answer:
(scroll down)

10,007,712 has 192 factors (divisors):
1; 2; 3; 4; 6; 8; 9; 11; 12; 13; 16; 18; 22; 24; 26; 27; 32; 33; 36; 39; 44; 48; 52; 54; 66; 72; 78; 81; 88; 96; 99; 104; 108; 117; 132; 143; 144; 156; 162; 176; 198; 208; 216; 234; 243; 264; 286; 288; 297; 312; 324; 351; 352; 396; 416; 429; 432; 468; 486; 528; 572; 594; 624; 648; 702; 729; 792; 858; 864; 891; 936; 972; 1,053; 1,056; 1,144; 1,188; 1,248; 1,287; 1,296; 1,404; 1,458; 1,584; 1,716; 1,782; 1,872; 1,944; 2,106; 2,187; 2,288; 2,376; 2,574; 2,592; 2,673; 2,808; 2,916; 3,159; 3,168; 3,432; 3,564; 3,744; 3,861; 3,888; 4,212; 4,374; 4,576; 4,752; 5,148; 5,346; 5,616; 5,832; 6,318; 6,864; 7,128; 7,722; 7,776; 8,019; 8,424; 8,748; 9,477; 9,504; 10,296; 10,692; 11,232; 11,583; 11,664; 12,636; 13,728; 14,256; 15,444; 16,038; 16,848; 17,496; 18,954; 20,592; 21,384; 23,166; 23,328; 24,057; 25,272; 28,431; 28,512; 30,888; 32,076; 33,696; 34,749; 34,992; 37,908; 41,184; 42,768; 46,332; 48,114; 50,544; 56,862; 61,776; 64,152; 69,498; 69,984; 75,816; 85,536; 92,664; 96,228; 101,088; 104,247; 113,724; 123,552; 128,304; 138,996; 151,632; 185,328; 192,456; 208,494; 227,448; 256,608; 277,992; 303,264; 312,741; 370,656; 384,912; 416,988; 454,896; 555,984; 625,482; 769,824; 833,976; 909,792; 1,111,968; 1,250,964; 1,667,952; 2,501,928; 3,335,904; 5,003,856 and 10,007,712
out of which 4 prime factors: 2; 3; 11 and 13
10,007,712 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.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 10,007,705?

» What are all the proper, improper and prime factors (divisors) of the number 10,007,727?


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".