Given the Number 9,090,900 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 9,090,900

1. Carry out the prime factorization of the number 9,090,900:

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


9,090,900 = 22 × 33 × 52 × 7 × 13 × 37
9,090,900 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 9,090,900

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
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
52 = 25
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
5 × 7 = 35
22 × 32 = 36
prime factor = 37
3 × 13 = 39
2 × 3 × 7 = 42
32 × 5 = 45
2 × 52 = 50
22 × 13 = 52
2 × 33 = 54
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 5 × 7 = 70
2 × 37 = 74
3 × 52 = 75
2 × 3 × 13 = 78
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
22 × 52 = 100
3 × 5 × 7 = 105
22 × 33 = 108
3 × 37 = 111
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
22 × 37 = 148
2 × 3 × 52 = 150
22 × 3 × 13 = 156
52 × 7 = 175
22 × 32 × 5 = 180
2 × 7 × 13 = 182
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
2 × 3 × 5 × 7 = 210
2 × 3 × 37 = 222
32 × 52 = 225
2 × 32 × 13 = 234
22 × 32 × 7 = 252
7 × 37 = 259
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
22 × 3 × 52 = 300
32 × 5 × 7 = 315
52 × 13 = 325
32 × 37 = 333
2 × 52 × 7 = 350
33 × 13 = 351
22 × 7 × 13 = 364
2 × 5 × 37 = 370
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
22 × 3 × 5 × 7 = 420
22 × 3 × 37 = 444
2 × 32 × 52 = 450
5 × 7 × 13 = 455
22 × 32 × 13 = 468
13 × 37 = 481
2 × 7 × 37 = 518
3 × 52 × 7 = 525
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
3 × 5 × 37 = 555
32 × 5 × 13 = 585
2 × 32 × 5 × 7 = 630
2 × 52 × 13 = 650
2 × 32 × 37 = 666
33 × 52 = 675
22 × 52 × 7 = 700
2 × 33 × 13 = 702
22 × 5 × 37 = 740
22 × 33 × 7 = 756
3 × 7 × 37 = 777
22 × 3 × 5 × 13 = 780
32 × 7 × 13 = 819
22 × 32 × 52 = 900
2 × 5 × 7 × 13 = 910
52 × 37 = 925
33 × 5 × 7 = 945
2 × 13 × 37 = 962
3 × 52 × 13 = 975
33 × 37 = 999
22 × 7 × 37 = 1,036
2 × 3 × 52 × 7 = 1,050
22 × 3 × 7 × 13 = 1,092
2 × 3 × 5 × 37 = 1,110
2 × 32 × 5 × 13 = 1,170
22 × 32 × 5 × 7 = 1,260
5 × 7 × 37 = 1,295
22 × 52 × 13 = 1,300
22 × 32 × 37 = 1,332
2 × 33 × 52 = 1,350
3 × 5 × 7 × 13 = 1,365
22 × 33 × 13 = 1,404
3 × 13 × 37 = 1,443
2 × 3 × 7 × 37 = 1,554
32 × 52 × 7 = 1,575
2 × 32 × 7 × 13 = 1,638
32 × 5 × 37 = 1,665
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 52 × 37 = 1,850
2 × 33 × 5 × 7 = 1,890
22 × 13 × 37 = 1,924
2 × 3 × 52 × 13 = 1,950
2 × 33 × 37 = 1,998
22 × 3 × 52 × 7 = 2,100
22 × 3 × 5 × 37 = 2,220
52 × 7 × 13 = 2,275
32 × 7 × 37 = 2,331
22 × 32 × 5 × 13 = 2,340
5 × 13 × 37 = 2,405
33 × 7 × 13 = 2,457
2 × 5 × 7 × 37 = 2,590
22 × 33 × 52 = 2,700
2 × 3 × 5 × 7 × 13 = 2,730
3 × 52 × 37 = 2,775
2 × 3 × 13 × 37 = 2,886
32 × 52 × 13 = 2,925
This list continues below...

... This list continues from above
22 × 3 × 7 × 37 = 3,108
2 × 32 × 52 × 7 = 3,150
22 × 32 × 7 × 13 = 3,276
2 × 32 × 5 × 37 = 3,330
7 × 13 × 37 = 3,367
2 × 33 × 5 × 13 = 3,510
22 × 52 × 37 = 3,700
22 × 33 × 5 × 7 = 3,780
3 × 5 × 7 × 37 = 3,885
22 × 3 × 52 × 13 = 3,900
22 × 33 × 37 = 3,996
32 × 5 × 7 × 13 = 4,095
32 × 13 × 37 = 4,329
2 × 52 × 7 × 13 = 4,550
2 × 32 × 7 × 37 = 4,662
33 × 52 × 7 = 4,725
2 × 5 × 13 × 37 = 4,810
2 × 33 × 7 × 13 = 4,914
33 × 5 × 37 = 4,995
22 × 5 × 7 × 37 = 5,180
22 × 3 × 5 × 7 × 13 = 5,460
2 × 3 × 52 × 37 = 5,550
22 × 3 × 13 × 37 = 5,772
2 × 32 × 52 × 13 = 5,850
22 × 32 × 52 × 7 = 6,300
52 × 7 × 37 = 6,475
22 × 32 × 5 × 37 = 6,660
2 × 7 × 13 × 37 = 6,734
3 × 52 × 7 × 13 = 6,825
33 × 7 × 37 = 6,993
22 × 33 × 5 × 13 = 7,020
3 × 5 × 13 × 37 = 7,215
2 × 3 × 5 × 7 × 37 = 7,770
2 × 32 × 5 × 7 × 13 = 8,190
32 × 52 × 37 = 8,325
2 × 32 × 13 × 37 = 8,658
33 × 52 × 13 = 8,775
22 × 52 × 7 × 13 = 9,100
22 × 32 × 7 × 37 = 9,324
2 × 33 × 52 × 7 = 9,450
22 × 5 × 13 × 37 = 9,620
22 × 33 × 7 × 13 = 9,828
2 × 33 × 5 × 37 = 9,990
3 × 7 × 13 × 37 = 10,101
22 × 3 × 52 × 37 = 11,100
32 × 5 × 7 × 37 = 11,655
22 × 32 × 52 × 13 = 11,700
52 × 13 × 37 = 12,025
33 × 5 × 7 × 13 = 12,285
2 × 52 × 7 × 37 = 12,950
33 × 13 × 37 = 12,987
22 × 7 × 13 × 37 = 13,468
2 × 3 × 52 × 7 × 13 = 13,650
2 × 33 × 7 × 37 = 13,986
2 × 3 × 5 × 13 × 37 = 14,430
22 × 3 × 5 × 7 × 37 = 15,540
22 × 32 × 5 × 7 × 13 = 16,380
2 × 32 × 52 × 37 = 16,650
5 × 7 × 13 × 37 = 16,835
22 × 32 × 13 × 37 = 17,316
2 × 33 × 52 × 13 = 17,550
22 × 33 × 52 × 7 = 18,900
3 × 52 × 7 × 37 = 19,425
22 × 33 × 5 × 37 = 19,980
2 × 3 × 7 × 13 × 37 = 20,202
32 × 52 × 7 × 13 = 20,475
32 × 5 × 13 × 37 = 21,645
2 × 32 × 5 × 7 × 37 = 23,310
2 × 52 × 13 × 37 = 24,050
2 × 33 × 5 × 7 × 13 = 24,570
33 × 52 × 37 = 24,975
22 × 52 × 7 × 37 = 25,900
2 × 33 × 13 × 37 = 25,974
22 × 3 × 52 × 7 × 13 = 27,300
22 × 33 × 7 × 37 = 27,972
22 × 3 × 5 × 13 × 37 = 28,860
32 × 7 × 13 × 37 = 30,303
22 × 32 × 52 × 37 = 33,300
2 × 5 × 7 × 13 × 37 = 33,670
33 × 5 × 7 × 37 = 34,965
22 × 33 × 52 × 13 = 35,100
3 × 52 × 13 × 37 = 36,075
2 × 3 × 52 × 7 × 37 = 38,850
22 × 3 × 7 × 13 × 37 = 40,404
2 × 32 × 52 × 7 × 13 = 40,950
2 × 32 × 5 × 13 × 37 = 43,290
22 × 32 × 5 × 7 × 37 = 46,620
22 × 52 × 13 × 37 = 48,100
22 × 33 × 5 × 7 × 13 = 49,140
2 × 33 × 52 × 37 = 49,950
3 × 5 × 7 × 13 × 37 = 50,505
22 × 33 × 13 × 37 = 51,948
32 × 52 × 7 × 37 = 58,275
2 × 32 × 7 × 13 × 37 = 60,606
33 × 52 × 7 × 13 = 61,425
33 × 5 × 13 × 37 = 64,935
22 × 5 × 7 × 13 × 37 = 67,340
2 × 33 × 5 × 7 × 37 = 69,930
2 × 3 × 52 × 13 × 37 = 72,150
22 × 3 × 52 × 7 × 37 = 77,700
22 × 32 × 52 × 7 × 13 = 81,900
52 × 7 × 13 × 37 = 84,175
22 × 32 × 5 × 13 × 37 = 86,580
33 × 7 × 13 × 37 = 90,909
22 × 33 × 52 × 37 = 99,900
2 × 3 × 5 × 7 × 13 × 37 = 101,010
32 × 52 × 13 × 37 = 108,225
2 × 32 × 52 × 7 × 37 = 116,550
22 × 32 × 7 × 13 × 37 = 121,212
2 × 33 × 52 × 7 × 13 = 122,850
2 × 33 × 5 × 13 × 37 = 129,870
22 × 33 × 5 × 7 × 37 = 139,860
22 × 3 × 52 × 13 × 37 = 144,300
32 × 5 × 7 × 13 × 37 = 151,515
2 × 52 × 7 × 13 × 37 = 168,350
33 × 52 × 7 × 37 = 174,825
2 × 33 × 7 × 13 × 37 = 181,818
22 × 3 × 5 × 7 × 13 × 37 = 202,020
2 × 32 × 52 × 13 × 37 = 216,450
22 × 32 × 52 × 7 × 37 = 233,100
22 × 33 × 52 × 7 × 13 = 245,700
3 × 52 × 7 × 13 × 37 = 252,525
22 × 33 × 5 × 13 × 37 = 259,740
2 × 32 × 5 × 7 × 13 × 37 = 303,030
33 × 52 × 13 × 37 = 324,675
22 × 52 × 7 × 13 × 37 = 336,700
2 × 33 × 52 × 7 × 37 = 349,650
22 × 33 × 7 × 13 × 37 = 363,636
22 × 32 × 52 × 13 × 37 = 432,900
33 × 5 × 7 × 13 × 37 = 454,545
2 × 3 × 52 × 7 × 13 × 37 = 505,050
22 × 32 × 5 × 7 × 13 × 37 = 606,060
2 × 33 × 52 × 13 × 37 = 649,350
22 × 33 × 52 × 7 × 37 = 699,300
32 × 52 × 7 × 13 × 37 = 757,575
2 × 33 × 5 × 7 × 13 × 37 = 909,090
22 × 3 × 52 × 7 × 13 × 37 = 1,010,100
22 × 33 × 52 × 13 × 37 = 1,298,700
2 × 32 × 52 × 7 × 13 × 37 = 1,515,150
22 × 33 × 5 × 7 × 13 × 37 = 1,818,180
33 × 52 × 7 × 13 × 37 = 2,272,725
22 × 32 × 52 × 7 × 13 × 37 = 3,030,300
2 × 33 × 52 × 7 × 13 × 37 = 4,545,450
22 × 33 × 52 × 7 × 13 × 37 = 9,090,900

The final answer:
(scroll down)

9,090,900 has 288 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 12; 13; 14; 15; 18; 20; 21; 25; 26; 27; 28; 30; 35; 36; 37; 39; 42; 45; 50; 52; 54; 60; 63; 65; 70; 74; 75; 78; 84; 90; 91; 100; 105; 108; 111; 117; 126; 130; 135; 140; 148; 150; 156; 175; 180; 182; 185; 189; 195; 210; 222; 225; 234; 252; 259; 260; 270; 273; 300; 315; 325; 333; 350; 351; 364; 370; 378; 390; 420; 444; 450; 455; 468; 481; 518; 525; 540; 546; 555; 585; 630; 650; 666; 675; 700; 702; 740; 756; 777; 780; 819; 900; 910; 925; 945; 962; 975; 999; 1,036; 1,050; 1,092; 1,110; 1,170; 1,260; 1,295; 1,300; 1,332; 1,350; 1,365; 1,404; 1,443; 1,554; 1,575; 1,638; 1,665; 1,755; 1,820; 1,850; 1,890; 1,924; 1,950; 1,998; 2,100; 2,220; 2,275; 2,331; 2,340; 2,405; 2,457; 2,590; 2,700; 2,730; 2,775; 2,886; 2,925; 3,108; 3,150; 3,276; 3,330; 3,367; 3,510; 3,700; 3,780; 3,885; 3,900; 3,996; 4,095; 4,329; 4,550; 4,662; 4,725; 4,810; 4,914; 4,995; 5,180; 5,460; 5,550; 5,772; 5,850; 6,300; 6,475; 6,660; 6,734; 6,825; 6,993; 7,020; 7,215; 7,770; 8,190; 8,325; 8,658; 8,775; 9,100; 9,324; 9,450; 9,620; 9,828; 9,990; 10,101; 11,100; 11,655; 11,700; 12,025; 12,285; 12,950; 12,987; 13,468; 13,650; 13,986; 14,430; 15,540; 16,380; 16,650; 16,835; 17,316; 17,550; 18,900; 19,425; 19,980; 20,202; 20,475; 21,645; 23,310; 24,050; 24,570; 24,975; 25,900; 25,974; 27,300; 27,972; 28,860; 30,303; 33,300; 33,670; 34,965; 35,100; 36,075; 38,850; 40,404; 40,950; 43,290; 46,620; 48,100; 49,140; 49,950; 50,505; 51,948; 58,275; 60,606; 61,425; 64,935; 67,340; 69,930; 72,150; 77,700; 81,900; 84,175; 86,580; 90,909; 99,900; 101,010; 108,225; 116,550; 121,212; 122,850; 129,870; 139,860; 144,300; 151,515; 168,350; 174,825; 181,818; 202,020; 216,450; 233,100; 245,700; 252,525; 259,740; 303,030; 324,675; 336,700; 349,650; 363,636; 432,900; 454,545; 505,050; 606,060; 649,350; 699,300; 757,575; 909,090; 1,010,100; 1,298,700; 1,515,150; 1,818,180; 2,272,725; 3,030,300; 4,545,450 and 9,090,900
out of which 6 prime factors: 2; 3; 5; 7; 13 and 37
9,090,900 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".