Given the Number 1,538,460 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 1,538,460

1. Carry out the prime factorization of the number 1,538,460:

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


1,538,460 = 22 × 33 × 5 × 7 × 11 × 37
1,538,460 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 1,538,460

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
prime factor = 5
2 × 3 = 6
prime factor = 7
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
prime factor = 37
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
2 × 33 = 54
5 × 11 = 55
22 × 3 × 5 = 60
32 × 7 = 63
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
7 × 11 = 77
22 × 3 × 7 = 84
2 × 32 × 5 = 90
32 × 11 = 99
3 × 5 × 7 = 105
22 × 33 = 108
2 × 5 × 11 = 110
3 × 37 = 111
2 × 32 × 7 = 126
22 × 3 × 11 = 132
33 × 5 = 135
22 × 5 × 7 = 140
22 × 37 = 148
2 × 7 × 11 = 154
3 × 5 × 11 = 165
22 × 32 × 5 = 180
5 × 37 = 185
33 × 7 = 189
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
22 × 5 × 11 = 220
2 × 3 × 37 = 222
3 × 7 × 11 = 231
22 × 32 × 7 = 252
7 × 37 = 259
2 × 33 × 5 = 270
33 × 11 = 297
22 × 7 × 11 = 308
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
32 × 37 = 333
2 × 5 × 37 = 370
2 × 33 × 7 = 378
5 × 7 × 11 = 385
22 × 32 × 11 = 396
11 × 37 = 407
22 × 3 × 5 × 7 = 420
22 × 3 × 37 = 444
2 × 3 × 7 × 11 = 462
32 × 5 × 11 = 495
2 × 7 × 37 = 518
22 × 33 × 5 = 540
3 × 5 × 37 = 555
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
22 × 3 × 5 × 11 = 660
2 × 32 × 37 = 666
32 × 7 × 11 = 693
22 × 5 × 37 = 740
22 × 33 × 7 = 756
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
2 × 11 × 37 = 814
22 × 3 × 7 × 11 = 924
33 × 5 × 7 = 945
2 × 32 × 5 × 11 = 990
33 × 37 = 999
22 × 7 × 37 = 1,036
2 × 3 × 5 × 37 = 1,110
3 × 5 × 7 × 11 = 1,155
22 × 33 × 11 = 1,188
3 × 11 × 37 = 1,221
This list continues below...

... This list continues from above
22 × 32 × 5 × 7 = 1,260
5 × 7 × 37 = 1,295
22 × 32 × 37 = 1,332
2 × 32 × 7 × 11 = 1,386
33 × 5 × 11 = 1,485
22 × 5 × 7 × 11 = 1,540
2 × 3 × 7 × 37 = 1,554
22 × 11 × 37 = 1,628
32 × 5 × 37 = 1,665
2 × 33 × 5 × 7 = 1,890
22 × 32 × 5 × 11 = 1,980
2 × 33 × 37 = 1,998
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
22 × 3 × 5 × 37 = 2,220
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
2 × 3 × 11 × 37 = 2,442
2 × 5 × 7 × 37 = 2,590
22 × 32 × 7 × 11 = 2,772
7 × 11 × 37 = 2,849
2 × 33 × 5 × 11 = 2,970
22 × 3 × 7 × 37 = 3,108
2 × 32 × 5 × 37 = 3,330
32 × 5 × 7 × 11 = 3,465
32 × 11 × 37 = 3,663
22 × 33 × 5 × 7 = 3,780
3 × 5 × 7 × 37 = 3,885
22 × 33 × 37 = 3,996
2 × 5 × 11 × 37 = 4,070
2 × 33 × 7 × 11 = 4,158
22 × 3 × 5 × 7 × 11 = 4,620
2 × 32 × 7 × 37 = 4,662
22 × 3 × 11 × 37 = 4,884
33 × 5 × 37 = 4,995
22 × 5 × 7 × 37 = 5,180
2 × 7 × 11 × 37 = 5,698
22 × 33 × 5 × 11 = 5,940
3 × 5 × 11 × 37 = 6,105
22 × 32 × 5 × 37 = 6,660
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
22 × 5 × 11 × 37 = 8,140
22 × 33 × 7 × 11 = 8,316
3 × 7 × 11 × 37 = 8,547
22 × 32 × 7 × 37 = 9,324
2 × 33 × 5 × 37 = 9,990
33 × 5 × 7 × 11 = 10,395
33 × 11 × 37 = 10,989
22 × 7 × 11 × 37 = 11,396
32 × 5 × 7 × 37 = 11,655
2 × 3 × 5 × 11 × 37 = 12,210
22 × 32 × 5 × 7 × 11 = 13,860
2 × 33 × 7 × 37 = 13,986
5 × 7 × 11 × 37 = 14,245
22 × 32 × 11 × 37 = 14,652
22 × 3 × 5 × 7 × 37 = 15,540
2 × 3 × 7 × 11 × 37 = 17,094
32 × 5 × 11 × 37 = 18,315
22 × 33 × 5 × 37 = 19,980
2 × 33 × 5 × 7 × 11 = 20,790
2 × 33 × 11 × 37 = 21,978
2 × 32 × 5 × 7 × 37 = 23,310
22 × 3 × 5 × 11 × 37 = 24,420
32 × 7 × 11 × 37 = 25,641
22 × 33 × 7 × 37 = 27,972
2 × 5 × 7 × 11 × 37 = 28,490
22 × 3 × 7 × 11 × 37 = 34,188
33 × 5 × 7 × 37 = 34,965
2 × 32 × 5 × 11 × 37 = 36,630
22 × 33 × 5 × 7 × 11 = 41,580
3 × 5 × 7 × 11 × 37 = 42,735
22 × 33 × 11 × 37 = 43,956
22 × 32 × 5 × 7 × 37 = 46,620
2 × 32 × 7 × 11 × 37 = 51,282
33 × 5 × 11 × 37 = 54,945
22 × 5 × 7 × 11 × 37 = 56,980
2 × 33 × 5 × 7 × 37 = 69,930
22 × 32 × 5 × 11 × 37 = 73,260
33 × 7 × 11 × 37 = 76,923
2 × 3 × 5 × 7 × 11 × 37 = 85,470
22 × 32 × 7 × 11 × 37 = 102,564
2 × 33 × 5 × 11 × 37 = 109,890
32 × 5 × 7 × 11 × 37 = 128,205
22 × 33 × 5 × 7 × 37 = 139,860
2 × 33 × 7 × 11 × 37 = 153,846
22 × 3 × 5 × 7 × 11 × 37 = 170,940
22 × 33 × 5 × 11 × 37 = 219,780
2 × 32 × 5 × 7 × 11 × 37 = 256,410
22 × 33 × 7 × 11 × 37 = 307,692
33 × 5 × 7 × 11 × 37 = 384,615
22 × 32 × 5 × 7 × 11 × 37 = 512,820
2 × 33 × 5 × 7 × 11 × 37 = 769,230
22 × 33 × 5 × 7 × 11 × 37 = 1,538,460

The final answer:
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1,538,460 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 11; 12; 14; 15; 18; 20; 21; 22; 27; 28; 30; 33; 35; 36; 37; 42; 44; 45; 54; 55; 60; 63; 66; 70; 74; 77; 84; 90; 99; 105; 108; 110; 111; 126; 132; 135; 140; 148; 154; 165; 180; 185; 189; 198; 210; 220; 222; 231; 252; 259; 270; 297; 308; 315; 330; 333; 370; 378; 385; 396; 407; 420; 444; 462; 495; 518; 540; 555; 594; 630; 660; 666; 693; 740; 756; 770; 777; 814; 924; 945; 990; 999; 1,036; 1,110; 1,155; 1,188; 1,221; 1,260; 1,295; 1,332; 1,386; 1,485; 1,540; 1,554; 1,628; 1,665; 1,890; 1,980; 1,998; 2,035; 2,079; 2,220; 2,310; 2,331; 2,442; 2,590; 2,772; 2,849; 2,970; 3,108; 3,330; 3,465; 3,663; 3,780; 3,885; 3,996; 4,070; 4,158; 4,620; 4,662; 4,884; 4,995; 5,180; 5,698; 5,940; 6,105; 6,660; 6,930; 6,993; 7,326; 7,770; 8,140; 8,316; 8,547; 9,324; 9,990; 10,395; 10,989; 11,396; 11,655; 12,210; 13,860; 13,986; 14,245; 14,652; 15,540; 17,094; 18,315; 19,980; 20,790; 21,978; 23,310; 24,420; 25,641; 27,972; 28,490; 34,188; 34,965; 36,630; 41,580; 42,735; 43,956; 46,620; 51,282; 54,945; 56,980; 69,930; 73,260; 76,923; 85,470; 102,564; 109,890; 128,205; 139,860; 153,846; 170,940; 219,780; 256,410; 307,692; 384,615; 512,820; 769,230 and 1,538,460
out of which 6 prime factors: 2; 3; 5; 7; 11 and 37
1,538,460 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".