Given the Number 20,769,210 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 20,769,210

1. Carry out the prime factorization of the number 20,769,210:

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


20,769,210 = 2 × 36 × 5 × 7 × 11 × 37
20,769,210 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 20,769,210

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
prime factor = 5
2 × 3 = 6
prime factor = 7
32 = 9
2 × 5 = 10
prime factor = 11
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
3 × 7 = 21
2 × 11 = 22
33 = 27
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
prime factor = 37
2 × 3 × 7 = 42
32 × 5 = 45
2 × 33 = 54
5 × 11 = 55
32 × 7 = 63
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
7 × 11 = 77
34 = 81
2 × 32 × 5 = 90
32 × 11 = 99
3 × 5 × 7 = 105
2 × 5 × 11 = 110
3 × 37 = 111
2 × 32 × 7 = 126
33 × 5 = 135
2 × 7 × 11 = 154
2 × 34 = 162
3 × 5 × 11 = 165
5 × 37 = 185
33 × 7 = 189
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
2 × 3 × 37 = 222
3 × 7 × 11 = 231
35 = 243
7 × 37 = 259
2 × 33 × 5 = 270
33 × 11 = 297
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
32 × 37 = 333
2 × 5 × 37 = 370
2 × 33 × 7 = 378
5 × 7 × 11 = 385
34 × 5 = 405
11 × 37 = 407
2 × 3 × 7 × 11 = 462
2 × 35 = 486
32 × 5 × 11 = 495
2 × 7 × 37 = 518
3 × 5 × 37 = 555
34 × 7 = 567
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
2 × 32 × 37 = 666
32 × 7 × 11 = 693
36 = 729
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
2 × 34 × 5 = 810
2 × 11 × 37 = 814
34 × 11 = 891
33 × 5 × 7 = 945
2 × 32 × 5 × 11 = 990
33 × 37 = 999
2 × 3 × 5 × 37 = 1,110
2 × 34 × 7 = 1,134
3 × 5 × 7 × 11 = 1,155
35 × 5 = 1,215
3 × 11 × 37 = 1,221
5 × 7 × 37 = 1,295
2 × 32 × 7 × 11 = 1,386
2 × 36 = 1,458
33 × 5 × 11 = 1,485
2 × 3 × 7 × 37 = 1,554
32 × 5 × 37 = 1,665
35 × 7 = 1,701
2 × 34 × 11 = 1,782
2 × 33 × 5 × 7 = 1,890
2 × 33 × 37 = 1,998
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
2 × 35 × 5 = 2,430
2 × 3 × 11 × 37 = 2,442
2 × 5 × 7 × 37 = 2,590
35 × 11 = 2,673
34 × 5 × 7 = 2,835
7 × 11 × 37 = 2,849
2 × 33 × 5 × 11 = 2,970
34 × 37 = 2,997
2 × 32 × 5 × 37 = 3,330
2 × 35 × 7 = 3,402
32 × 5 × 7 × 11 = 3,465
36 × 5 = 3,645
32 × 11 × 37 = 3,663
3 × 5 × 7 × 37 = 3,885
2 × 5 × 11 × 37 = 4,070
2 × 33 × 7 × 11 = 4,158
34 × 5 × 11 = 4,455
This list continues below...

... This list continues from above
2 × 32 × 7 × 37 = 4,662
33 × 5 × 37 = 4,995
36 × 7 = 5,103
2 × 35 × 11 = 5,346
2 × 34 × 5 × 7 = 5,670
2 × 7 × 11 × 37 = 5,698
2 × 34 × 37 = 5,994
3 × 5 × 11 × 37 = 6,105
34 × 7 × 11 = 6,237
2 × 32 × 5 × 7 × 11 = 6,930
33 × 7 × 37 = 6,993
2 × 36 × 5 = 7,290
2 × 32 × 11 × 37 = 7,326
2 × 3 × 5 × 7 × 37 = 7,770
36 × 11 = 8,019
35 × 5 × 7 = 8,505
3 × 7 × 11 × 37 = 8,547
2 × 34 × 5 × 11 = 8,910
35 × 37 = 8,991
2 × 33 × 5 × 37 = 9,990
2 × 36 × 7 = 10,206
33 × 5 × 7 × 11 = 10,395
33 × 11 × 37 = 10,989
32 × 5 × 7 × 37 = 11,655
2 × 3 × 5 × 11 × 37 = 12,210
2 × 34 × 7 × 11 = 12,474
35 × 5 × 11 = 13,365
2 × 33 × 7 × 37 = 13,986
5 × 7 × 11 × 37 = 14,245
34 × 5 × 37 = 14,985
2 × 36 × 11 = 16,038
2 × 35 × 5 × 7 = 17,010
2 × 3 × 7 × 11 × 37 = 17,094
2 × 35 × 37 = 17,982
32 × 5 × 11 × 37 = 18,315
35 × 7 × 11 = 18,711
2 × 33 × 5 × 7 × 11 = 20,790
34 × 7 × 37 = 20,979
2 × 33 × 11 × 37 = 21,978
2 × 32 × 5 × 7 × 37 = 23,310
36 × 5 × 7 = 25,515
32 × 7 × 11 × 37 = 25,641
2 × 35 × 5 × 11 = 26,730
36 × 37 = 26,973
2 × 5 × 7 × 11 × 37 = 28,490
2 × 34 × 5 × 37 = 29,970
34 × 5 × 7 × 11 = 31,185
34 × 11 × 37 = 32,967
33 × 5 × 7 × 37 = 34,965
2 × 32 × 5 × 11 × 37 = 36,630
2 × 35 × 7 × 11 = 37,422
36 × 5 × 11 = 40,095
2 × 34 × 7 × 37 = 41,958
3 × 5 × 7 × 11 × 37 = 42,735
35 × 5 × 37 = 44,955
2 × 36 × 5 × 7 = 51,030
2 × 32 × 7 × 11 × 37 = 51,282
2 × 36 × 37 = 53,946
33 × 5 × 11 × 37 = 54,945
36 × 7 × 11 = 56,133
2 × 34 × 5 × 7 × 11 = 62,370
35 × 7 × 37 = 62,937
2 × 34 × 11 × 37 = 65,934
2 × 33 × 5 × 7 × 37 = 69,930
33 × 7 × 11 × 37 = 76,923
2 × 36 × 5 × 11 = 80,190
2 × 3 × 5 × 7 × 11 × 37 = 85,470
2 × 35 × 5 × 37 = 89,910
35 × 5 × 7 × 11 = 93,555
35 × 11 × 37 = 98,901
34 × 5 × 7 × 37 = 104,895
2 × 33 × 5 × 11 × 37 = 109,890
2 × 36 × 7 × 11 = 112,266
2 × 35 × 7 × 37 = 125,874
32 × 5 × 7 × 11 × 37 = 128,205
36 × 5 × 37 = 134,865
2 × 33 × 7 × 11 × 37 = 153,846
34 × 5 × 11 × 37 = 164,835
2 × 35 × 5 × 7 × 11 = 187,110
36 × 7 × 37 = 188,811
2 × 35 × 11 × 37 = 197,802
2 × 34 × 5 × 7 × 37 = 209,790
34 × 7 × 11 × 37 = 230,769
2 × 32 × 5 × 7 × 11 × 37 = 256,410
2 × 36 × 5 × 37 = 269,730
36 × 5 × 7 × 11 = 280,665
36 × 11 × 37 = 296,703
35 × 5 × 7 × 37 = 314,685
2 × 34 × 5 × 11 × 37 = 329,670
2 × 36 × 7 × 37 = 377,622
33 × 5 × 7 × 11 × 37 = 384,615
2 × 34 × 7 × 11 × 37 = 461,538
35 × 5 × 11 × 37 = 494,505
2 × 36 × 5 × 7 × 11 = 561,330
2 × 36 × 11 × 37 = 593,406
2 × 35 × 5 × 7 × 37 = 629,370
35 × 7 × 11 × 37 = 692,307
2 × 33 × 5 × 7 × 11 × 37 = 769,230
36 × 5 × 7 × 37 = 944,055
2 × 35 × 5 × 11 × 37 = 989,010
34 × 5 × 7 × 11 × 37 = 1,153,845
2 × 35 × 7 × 11 × 37 = 1,384,614
36 × 5 × 11 × 37 = 1,483,515
2 × 36 × 5 × 7 × 37 = 1,888,110
36 × 7 × 11 × 37 = 2,076,921
2 × 34 × 5 × 7 × 11 × 37 = 2,307,690
2 × 36 × 5 × 11 × 37 = 2,967,030
35 × 5 × 7 × 11 × 37 = 3,461,535
2 × 36 × 7 × 11 × 37 = 4,153,842
2 × 35 × 5 × 7 × 11 × 37 = 6,923,070
36 × 5 × 7 × 11 × 37 = 10,384,605
2 × 36 × 5 × 7 × 11 × 37 = 20,769,210

The final answer:
(scroll down)

20,769,210 has 224 factors (divisors):
1; 2; 3; 5; 6; 7; 9; 10; 11; 14; 15; 18; 21; 22; 27; 30; 33; 35; 37; 42; 45; 54; 55; 63; 66; 70; 74; 77; 81; 90; 99; 105; 110; 111; 126; 135; 154; 162; 165; 185; 189; 198; 210; 222; 231; 243; 259; 270; 297; 315; 330; 333; 370; 378; 385; 405; 407; 462; 486; 495; 518; 555; 567; 594; 630; 666; 693; 729; 770; 777; 810; 814; 891; 945; 990; 999; 1,110; 1,134; 1,155; 1,215; 1,221; 1,295; 1,386; 1,458; 1,485; 1,554; 1,665; 1,701; 1,782; 1,890; 1,998; 2,035; 2,079; 2,310; 2,331; 2,430; 2,442; 2,590; 2,673; 2,835; 2,849; 2,970; 2,997; 3,330; 3,402; 3,465; 3,645; 3,663; 3,885; 4,070; 4,158; 4,455; 4,662; 4,995; 5,103; 5,346; 5,670; 5,698; 5,994; 6,105; 6,237; 6,930; 6,993; 7,290; 7,326; 7,770; 8,019; 8,505; 8,547; 8,910; 8,991; 9,990; 10,206; 10,395; 10,989; 11,655; 12,210; 12,474; 13,365; 13,986; 14,245; 14,985; 16,038; 17,010; 17,094; 17,982; 18,315; 18,711; 20,790; 20,979; 21,978; 23,310; 25,515; 25,641; 26,730; 26,973; 28,490; 29,970; 31,185; 32,967; 34,965; 36,630; 37,422; 40,095; 41,958; 42,735; 44,955; 51,030; 51,282; 53,946; 54,945; 56,133; 62,370; 62,937; 65,934; 69,930; 76,923; 80,190; 85,470; 89,910; 93,555; 98,901; 104,895; 109,890; 112,266; 125,874; 128,205; 134,865; 153,846; 164,835; 187,110; 188,811; 197,802; 209,790; 230,769; 256,410; 269,730; 280,665; 296,703; 314,685; 329,670; 377,622; 384,615; 461,538; 494,505; 561,330; 593,406; 629,370; 692,307; 769,230; 944,055; 989,010; 1,153,845; 1,384,614; 1,483,515; 1,888,110; 2,076,921; 2,307,690; 2,967,030; 3,461,535; 4,153,842; 6,923,070; 10,384,605 and 20,769,210
out of which 6 prime factors: 2; 3; 5; 7; 11 and 37
20,769,210 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".