Given the Number 6,923,070 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 6,923,070

1. Carry out the prime factorization of the number 6,923,070:

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


6,923,070 = 2 × 35 × 5 × 7 × 11 × 37
6,923,070 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 6,923,070

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
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
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
This list continues below...

... This list continues from above
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
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
2 × 32 × 7 × 37 = 4,662
33 × 5 × 37 = 4,995
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 × 32 × 11 × 37 = 7,326
2 × 3 × 5 × 7 × 37 = 7,770
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
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 × 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
32 × 7 × 11 × 37 = 25,641
2 × 35 × 5 × 11 = 26,730
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
2 × 34 × 7 × 37 = 41,958
3 × 5 × 7 × 11 × 37 = 42,735
35 × 5 × 37 = 44,955
2 × 32 × 7 × 11 × 37 = 51,282
33 × 5 × 11 × 37 = 54,945
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 × 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 × 35 × 7 × 37 = 125,874
32 × 5 × 7 × 11 × 37 = 128,205
2 × 33 × 7 × 11 × 37 = 153,846
34 × 5 × 11 × 37 = 164,835
2 × 35 × 5 × 7 × 11 = 187,110
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
35 × 5 × 7 × 37 = 314,685
2 × 34 × 5 × 11 × 37 = 329,670
33 × 5 × 7 × 11 × 37 = 384,615
2 × 34 × 7 × 11 × 37 = 461,538
35 × 5 × 11 × 37 = 494,505
2 × 35 × 5 × 7 × 37 = 629,370
35 × 7 × 11 × 37 = 692,307
2 × 33 × 5 × 7 × 11 × 37 = 769,230
2 × 35 × 5 × 11 × 37 = 989,010
34 × 5 × 7 × 11 × 37 = 1,153,845
2 × 35 × 7 × 11 × 37 = 1,384,614
2 × 34 × 5 × 7 × 11 × 37 = 2,307,690
35 × 5 × 7 × 11 × 37 = 3,461,535
2 × 35 × 5 × 7 × 11 × 37 = 6,923,070

The final answer:
(scroll down)

6,923,070 has 192 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; 770; 777; 810; 814; 891; 945; 990; 999; 1,110; 1,134; 1,155; 1,215; 1,221; 1,295; 1,386; 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; 3,663; 3,885; 4,070; 4,158; 4,455; 4,662; 4,995; 5,346; 5,670; 5,698; 5,994; 6,105; 6,237; 6,930; 6,993; 7,326; 7,770; 8,505; 8,547; 8,910; 8,991; 9,990; 10,395; 10,989; 11,655; 12,210; 12,474; 13,365; 13,986; 14,245; 14,985; 17,010; 17,094; 17,982; 18,315; 18,711; 20,790; 20,979; 21,978; 23,310; 25,641; 26,730; 28,490; 29,970; 31,185; 32,967; 34,965; 36,630; 37,422; 41,958; 42,735; 44,955; 51,282; 54,945; 62,370; 62,937; 65,934; 69,930; 76,923; 85,470; 89,910; 93,555; 98,901; 104,895; 109,890; 125,874; 128,205; 153,846; 164,835; 187,110; 197,802; 209,790; 230,769; 256,410; 314,685; 329,670; 384,615; 461,538; 494,505; 629,370; 692,307; 769,230; 989,010; 1,153,845; 1,384,614; 2,307,690; 3,461,535 and 6,923,070
out of which 6 prime factors: 2; 3; 5; 7; 11 and 37
6,923,070 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".