Given the Number 7,297,290 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 7,297,290

1. Carry out the prime factorization of the number 7,297,290:

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


7,297,290 = 2 × 36 × 5 × 7 × 11 × 13
7,297,290 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 7,297,290

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
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
3 × 7 = 21
2 × 11 = 22
2 × 13 = 26
33 = 27
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
3 × 13 = 39
2 × 3 × 7 = 42
32 × 5 = 45
2 × 33 = 54
5 × 11 = 55
32 × 7 = 63
5 × 13 = 65
2 × 3 × 11 = 66
2 × 5 × 7 = 70
7 × 11 = 77
2 × 3 × 13 = 78
34 = 81
2 × 32 × 5 = 90
7 × 13 = 91
32 × 11 = 99
3 × 5 × 7 = 105
2 × 5 × 11 = 110
32 × 13 = 117
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
11 × 13 = 143
2 × 7 × 11 = 154
2 × 34 = 162
3 × 5 × 11 = 165
2 × 7 × 13 = 182
33 × 7 = 189
3 × 5 × 13 = 195
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
3 × 7 × 11 = 231
2 × 32 × 13 = 234
35 = 243
2 × 33 × 5 = 270
3 × 7 × 13 = 273
2 × 11 × 13 = 286
33 × 11 = 297
32 × 5 × 7 = 315
2 × 3 × 5 × 11 = 330
33 × 13 = 351
2 × 33 × 7 = 378
5 × 7 × 11 = 385
2 × 3 × 5 × 13 = 390
34 × 5 = 405
3 × 11 × 13 = 429
5 × 7 × 13 = 455
2 × 3 × 7 × 11 = 462
2 × 35 = 486
32 × 5 × 11 = 495
2 × 3 × 7 × 13 = 546
34 × 7 = 567
32 × 5 × 13 = 585
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
32 × 7 × 11 = 693
2 × 33 × 13 = 702
5 × 11 × 13 = 715
36 = 729
2 × 5 × 7 × 11 = 770
2 × 34 × 5 = 810
32 × 7 × 13 = 819
2 × 3 × 11 × 13 = 858
34 × 11 = 891
2 × 5 × 7 × 13 = 910
33 × 5 × 7 = 945
2 × 32 × 5 × 11 = 990
7 × 11 × 13 = 1,001
34 × 13 = 1,053
2 × 34 × 7 = 1,134
3 × 5 × 7 × 11 = 1,155
2 × 32 × 5 × 13 = 1,170
35 × 5 = 1,215
32 × 11 × 13 = 1,287
3 × 5 × 7 × 13 = 1,365
2 × 32 × 7 × 11 = 1,386
2 × 5 × 11 × 13 = 1,430
2 × 36 = 1,458
33 × 5 × 11 = 1,485
2 × 32 × 7 × 13 = 1,638
35 × 7 = 1,701
33 × 5 × 13 = 1,755
2 × 34 × 11 = 1,782
2 × 33 × 5 × 7 = 1,890
2 × 7 × 11 × 13 = 2,002
33 × 7 × 11 = 2,079
2 × 34 × 13 = 2,106
3 × 5 × 11 × 13 = 2,145
2 × 3 × 5 × 7 × 11 = 2,310
2 × 35 × 5 = 2,430
33 × 7 × 13 = 2,457
2 × 32 × 11 × 13 = 2,574
35 × 11 = 2,673
This list continues below...

... This list continues from above
2 × 3 × 5 × 7 × 13 = 2,730
34 × 5 × 7 = 2,835
2 × 33 × 5 × 11 = 2,970
3 × 7 × 11 × 13 = 3,003
35 × 13 = 3,159
2 × 35 × 7 = 3,402
32 × 5 × 7 × 11 = 3,465
2 × 33 × 5 × 13 = 3,510
36 × 5 = 3,645
33 × 11 × 13 = 3,861
32 × 5 × 7 × 13 = 4,095
2 × 33 × 7 × 11 = 4,158
2 × 3 × 5 × 11 × 13 = 4,290
34 × 5 × 11 = 4,455
2 × 33 × 7 × 13 = 4,914
5 × 7 × 11 × 13 = 5,005
36 × 7 = 5,103
34 × 5 × 13 = 5,265
2 × 35 × 11 = 5,346
2 × 34 × 5 × 7 = 5,670
2 × 3 × 7 × 11 × 13 = 6,006
34 × 7 × 11 = 6,237
2 × 35 × 13 = 6,318
32 × 5 × 11 × 13 = 6,435
2 × 32 × 5 × 7 × 11 = 6,930
2 × 36 × 5 = 7,290
34 × 7 × 13 = 7,371
2 × 33 × 11 × 13 = 7,722
36 × 11 = 8,019
2 × 32 × 5 × 7 × 13 = 8,190
35 × 5 × 7 = 8,505
2 × 34 × 5 × 11 = 8,910
32 × 7 × 11 × 13 = 9,009
36 × 13 = 9,477
2 × 5 × 7 × 11 × 13 = 10,010
2 × 36 × 7 = 10,206
33 × 5 × 7 × 11 = 10,395
2 × 34 × 5 × 13 = 10,530
34 × 11 × 13 = 11,583
33 × 5 × 7 × 13 = 12,285
2 × 34 × 7 × 11 = 12,474
2 × 32 × 5 × 11 × 13 = 12,870
35 × 5 × 11 = 13,365
2 × 34 × 7 × 13 = 14,742
3 × 5 × 7 × 11 × 13 = 15,015
35 × 5 × 13 = 15,795
2 × 36 × 11 = 16,038
2 × 35 × 5 × 7 = 17,010
2 × 32 × 7 × 11 × 13 = 18,018
35 × 7 × 11 = 18,711
2 × 36 × 13 = 18,954
33 × 5 × 11 × 13 = 19,305
2 × 33 × 5 × 7 × 11 = 20,790
35 × 7 × 13 = 22,113
2 × 34 × 11 × 13 = 23,166
2 × 33 × 5 × 7 × 13 = 24,570
36 × 5 × 7 = 25,515
2 × 35 × 5 × 11 = 26,730
33 × 7 × 11 × 13 = 27,027
2 × 3 × 5 × 7 × 11 × 13 = 30,030
34 × 5 × 7 × 11 = 31,185
2 × 35 × 5 × 13 = 31,590
35 × 11 × 13 = 34,749
34 × 5 × 7 × 13 = 36,855
2 × 35 × 7 × 11 = 37,422
2 × 33 × 5 × 11 × 13 = 38,610
36 × 5 × 11 = 40,095
2 × 35 × 7 × 13 = 44,226
32 × 5 × 7 × 11 × 13 = 45,045
36 × 5 × 13 = 47,385
2 × 36 × 5 × 7 = 51,030
2 × 33 × 7 × 11 × 13 = 54,054
36 × 7 × 11 = 56,133
34 × 5 × 11 × 13 = 57,915
2 × 34 × 5 × 7 × 11 = 62,370
36 × 7 × 13 = 66,339
2 × 35 × 11 × 13 = 69,498
2 × 34 × 5 × 7 × 13 = 73,710
2 × 36 × 5 × 11 = 80,190
34 × 7 × 11 × 13 = 81,081
2 × 32 × 5 × 7 × 11 × 13 = 90,090
35 × 5 × 7 × 11 = 93,555
2 × 36 × 5 × 13 = 94,770
36 × 11 × 13 = 104,247
35 × 5 × 7 × 13 = 110,565
2 × 36 × 7 × 11 = 112,266
2 × 34 × 5 × 11 × 13 = 115,830
2 × 36 × 7 × 13 = 132,678
33 × 5 × 7 × 11 × 13 = 135,135
2 × 34 × 7 × 11 × 13 = 162,162
35 × 5 × 11 × 13 = 173,745
2 × 35 × 5 × 7 × 11 = 187,110
2 × 36 × 11 × 13 = 208,494
2 × 35 × 5 × 7 × 13 = 221,130
35 × 7 × 11 × 13 = 243,243
2 × 33 × 5 × 7 × 11 × 13 = 270,270
36 × 5 × 7 × 11 = 280,665
36 × 5 × 7 × 13 = 331,695
2 × 35 × 5 × 11 × 13 = 347,490
34 × 5 × 7 × 11 × 13 = 405,405
2 × 35 × 7 × 11 × 13 = 486,486
36 × 5 × 11 × 13 = 521,235
2 × 36 × 5 × 7 × 11 = 561,330
2 × 36 × 5 × 7 × 13 = 663,390
36 × 7 × 11 × 13 = 729,729
2 × 34 × 5 × 7 × 11 × 13 = 810,810
2 × 36 × 5 × 11 × 13 = 1,042,470
35 × 5 × 7 × 11 × 13 = 1,216,215
2 × 36 × 7 × 11 × 13 = 1,459,458
2 × 35 × 5 × 7 × 11 × 13 = 2,432,430
36 × 5 × 7 × 11 × 13 = 3,648,645
2 × 36 × 5 × 7 × 11 × 13 = 7,297,290

The final answer:
(scroll down)

7,297,290 has 224 factors (divisors):
1; 2; 3; 5; 6; 7; 9; 10; 11; 13; 14; 15; 18; 21; 22; 26; 27; 30; 33; 35; 39; 42; 45; 54; 55; 63; 65; 66; 70; 77; 78; 81; 90; 91; 99; 105; 110; 117; 126; 130; 135; 143; 154; 162; 165; 182; 189; 195; 198; 210; 231; 234; 243; 270; 273; 286; 297; 315; 330; 351; 378; 385; 390; 405; 429; 455; 462; 486; 495; 546; 567; 585; 594; 630; 693; 702; 715; 729; 770; 810; 819; 858; 891; 910; 945; 990; 1,001; 1,053; 1,134; 1,155; 1,170; 1,215; 1,287; 1,365; 1,386; 1,430; 1,458; 1,485; 1,638; 1,701; 1,755; 1,782; 1,890; 2,002; 2,079; 2,106; 2,145; 2,310; 2,430; 2,457; 2,574; 2,673; 2,730; 2,835; 2,970; 3,003; 3,159; 3,402; 3,465; 3,510; 3,645; 3,861; 4,095; 4,158; 4,290; 4,455; 4,914; 5,005; 5,103; 5,265; 5,346; 5,670; 6,006; 6,237; 6,318; 6,435; 6,930; 7,290; 7,371; 7,722; 8,019; 8,190; 8,505; 8,910; 9,009; 9,477; 10,010; 10,206; 10,395; 10,530; 11,583; 12,285; 12,474; 12,870; 13,365; 14,742; 15,015; 15,795; 16,038; 17,010; 18,018; 18,711; 18,954; 19,305; 20,790; 22,113; 23,166; 24,570; 25,515; 26,730; 27,027; 30,030; 31,185; 31,590; 34,749; 36,855; 37,422; 38,610; 40,095; 44,226; 45,045; 47,385; 51,030; 54,054; 56,133; 57,915; 62,370; 66,339; 69,498; 73,710; 80,190; 81,081; 90,090; 93,555; 94,770; 104,247; 110,565; 112,266; 115,830; 132,678; 135,135; 162,162; 173,745; 187,110; 208,494; 221,130; 243,243; 270,270; 280,665; 331,695; 347,490; 405,405; 486,486; 521,235; 561,330; 663,390; 729,729; 810,810; 1,042,470; 1,216,215; 1,459,458; 2,432,430; 3,648,645 and 7,297,290
out of which 6 prime factors: 2; 3; 5; 7; 11 and 13
7,297,290 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".