Given the Number 540,540 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 540,540

1. Carry out the prime factorization of the number 540,540:

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


540,540 = 22 × 33 × 5 × 7 × 11 × 13
540,540 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 540,540

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
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
3 × 13 = 39
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
22 × 13 = 52
2 × 33 = 54
5 × 11 = 55
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 3 × 11 = 66
2 × 5 × 7 = 70
7 × 11 = 77
2 × 3 × 13 = 78
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
32 × 11 = 99
3 × 5 × 7 = 105
22 × 33 = 108
2 × 5 × 11 = 110
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
22 × 3 × 11 = 132
33 × 5 = 135
22 × 5 × 7 = 140
11 × 13 = 143
2 × 7 × 11 = 154
22 × 3 × 13 = 156
3 × 5 × 11 = 165
22 × 32 × 5 = 180
2 × 7 × 13 = 182
33 × 7 = 189
3 × 5 × 13 = 195
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
22 × 5 × 11 = 220
3 × 7 × 11 = 231
2 × 32 × 13 = 234
22 × 32 × 7 = 252
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
22 × 7 × 11 = 308
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
33 × 13 = 351
22 × 7 × 13 = 364
2 × 33 × 7 = 378
5 × 7 × 11 = 385
2 × 3 × 5 × 13 = 390
22 × 32 × 11 = 396
22 × 3 × 5 × 7 = 420
3 × 11 × 13 = 429
5 × 7 × 13 = 455
2 × 3 × 7 × 11 = 462
22 × 32 × 13 = 468
32 × 5 × 11 = 495
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
22 × 11 × 13 = 572
32 × 5 × 13 = 585
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
22 × 3 × 5 × 11 = 660
32 × 7 × 11 = 693
2 × 33 × 13 = 702
5 × 11 × 13 = 715
This list continues below...

... This list continues from above
22 × 33 × 7 = 756
2 × 5 × 7 × 11 = 770
22 × 3 × 5 × 13 = 780
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
2 × 5 × 7 × 13 = 910
22 × 3 × 7 × 11 = 924
33 × 5 × 7 = 945
2 × 32 × 5 × 11 = 990
7 × 11 × 13 = 1,001
22 × 3 × 7 × 13 = 1,092
3 × 5 × 7 × 11 = 1,155
2 × 32 × 5 × 13 = 1,170
22 × 33 × 11 = 1,188
22 × 32 × 5 × 7 = 1,260
32 × 11 × 13 = 1,287
3 × 5 × 7 × 13 = 1,365
2 × 32 × 7 × 11 = 1,386
22 × 33 × 13 = 1,404
2 × 5 × 11 × 13 = 1,430
33 × 5 × 11 = 1,485
22 × 5 × 7 × 11 = 1,540
2 × 32 × 7 × 13 = 1,638
22 × 3 × 11 × 13 = 1,716
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 33 × 5 × 7 = 1,890
22 × 32 × 5 × 11 = 1,980
2 × 7 × 11 × 13 = 2,002
33 × 7 × 11 = 2,079
3 × 5 × 11 × 13 = 2,145
2 × 3 × 5 × 7 × 11 = 2,310
22 × 32 × 5 × 13 = 2,340
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
2 × 3 × 5 × 7 × 13 = 2,730
22 × 32 × 7 × 11 = 2,772
22 × 5 × 11 × 13 = 2,860
2 × 33 × 5 × 11 = 2,970
3 × 7 × 11 × 13 = 3,003
22 × 32 × 7 × 13 = 3,276
32 × 5 × 7 × 11 = 3,465
2 × 33 × 5 × 13 = 3,510
22 × 33 × 5 × 7 = 3,780
33 × 11 × 13 = 3,861
22 × 7 × 11 × 13 = 4,004
32 × 5 × 7 × 13 = 4,095
2 × 33 × 7 × 11 = 4,158
2 × 3 × 5 × 11 × 13 = 4,290
22 × 3 × 5 × 7 × 11 = 4,620
2 × 33 × 7 × 13 = 4,914
5 × 7 × 11 × 13 = 5,005
22 × 32 × 11 × 13 = 5,148
22 × 3 × 5 × 7 × 13 = 5,460
22 × 33 × 5 × 11 = 5,940
2 × 3 × 7 × 11 × 13 = 6,006
32 × 5 × 11 × 13 = 6,435
2 × 32 × 5 × 7 × 11 = 6,930
22 × 33 × 5 × 13 = 7,020
2 × 33 × 11 × 13 = 7,722
2 × 32 × 5 × 7 × 13 = 8,190
22 × 33 × 7 × 11 = 8,316
22 × 3 × 5 × 11 × 13 = 8,580
32 × 7 × 11 × 13 = 9,009
22 × 33 × 7 × 13 = 9,828
2 × 5 × 7 × 11 × 13 = 10,010
33 × 5 × 7 × 11 = 10,395
22 × 3 × 7 × 11 × 13 = 12,012
33 × 5 × 7 × 13 = 12,285
2 × 32 × 5 × 11 × 13 = 12,870
22 × 32 × 5 × 7 × 11 = 13,860
3 × 5 × 7 × 11 × 13 = 15,015
22 × 33 × 11 × 13 = 15,444
22 × 32 × 5 × 7 × 13 = 16,380
2 × 32 × 7 × 11 × 13 = 18,018
33 × 5 × 11 × 13 = 19,305
22 × 5 × 7 × 11 × 13 = 20,020
2 × 33 × 5 × 7 × 11 = 20,790
2 × 33 × 5 × 7 × 13 = 24,570
22 × 32 × 5 × 11 × 13 = 25,740
33 × 7 × 11 × 13 = 27,027
2 × 3 × 5 × 7 × 11 × 13 = 30,030
22 × 32 × 7 × 11 × 13 = 36,036
2 × 33 × 5 × 11 × 13 = 38,610
22 × 33 × 5 × 7 × 11 = 41,580
32 × 5 × 7 × 11 × 13 = 45,045
22 × 33 × 5 × 7 × 13 = 49,140
2 × 33 × 7 × 11 × 13 = 54,054
22 × 3 × 5 × 7 × 11 × 13 = 60,060
22 × 33 × 5 × 11 × 13 = 77,220
2 × 32 × 5 × 7 × 11 × 13 = 90,090
22 × 33 × 7 × 11 × 13 = 108,108
33 × 5 × 7 × 11 × 13 = 135,135
22 × 32 × 5 × 7 × 11 × 13 = 180,180
2 × 33 × 5 × 7 × 11 × 13 = 270,270
22 × 33 × 5 × 7 × 11 × 13 = 540,540

The final answer:
(scroll down)

540,540 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 11; 12; 13; 14; 15; 18; 20; 21; 22; 26; 27; 28; 30; 33; 35; 36; 39; 42; 44; 45; 52; 54; 55; 60; 63; 65; 66; 70; 77; 78; 84; 90; 91; 99; 105; 108; 110; 117; 126; 130; 132; 135; 140; 143; 154; 156; 165; 180; 182; 189; 195; 198; 210; 220; 231; 234; 252; 260; 270; 273; 286; 297; 308; 315; 330; 351; 364; 378; 385; 390; 396; 420; 429; 455; 462; 468; 495; 540; 546; 572; 585; 594; 630; 660; 693; 702; 715; 756; 770; 780; 819; 858; 910; 924; 945; 990; 1,001; 1,092; 1,155; 1,170; 1,188; 1,260; 1,287; 1,365; 1,386; 1,404; 1,430; 1,485; 1,540; 1,638; 1,716; 1,755; 1,820; 1,890; 1,980; 2,002; 2,079; 2,145; 2,310; 2,340; 2,457; 2,574; 2,730; 2,772; 2,860; 2,970; 3,003; 3,276; 3,465; 3,510; 3,780; 3,861; 4,004; 4,095; 4,158; 4,290; 4,620; 4,914; 5,005; 5,148; 5,460; 5,940; 6,006; 6,435; 6,930; 7,020; 7,722; 8,190; 8,316; 8,580; 9,009; 9,828; 10,010; 10,395; 12,012; 12,285; 12,870; 13,860; 15,015; 15,444; 16,380; 18,018; 19,305; 20,020; 20,790; 24,570; 25,740; 27,027; 30,030; 36,036; 38,610; 41,580; 45,045; 49,140; 54,054; 60,060; 77,220; 90,090; 108,108; 135,135; 180,180; 270,270 and 540,540
out of which 6 prime factors: 2; 3; 5; 7; 11 and 13
540,540 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".