Given the Number 21,410,480 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 21,410,480

1. Carry out the prime factorization of the number 21,410,480:

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


21,410,480 = 24 × 5 × 7 × 13 × 17 × 173
21,410,480 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 21,410,480

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
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
prime factor = 13
2 × 7 = 14
24 = 16
prime factor = 17
22 × 5 = 20
2 × 13 = 26
22 × 7 = 28
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
22 × 13 = 52
23 × 7 = 56
5 × 13 = 65
22 × 17 = 68
2 × 5 × 7 = 70
24 × 5 = 80
5 × 17 = 85
7 × 13 = 91
23 × 13 = 104
24 × 7 = 112
7 × 17 = 119
2 × 5 × 13 = 130
23 × 17 = 136
22 × 5 × 7 = 140
2 × 5 × 17 = 170
prime factor = 173
2 × 7 × 13 = 182
24 × 13 = 208
13 × 17 = 221
2 × 7 × 17 = 238
22 × 5 × 13 = 260
24 × 17 = 272
23 × 5 × 7 = 280
22 × 5 × 17 = 340
2 × 173 = 346
22 × 7 × 13 = 364
2 × 13 × 17 = 442
5 × 7 × 13 = 455
22 × 7 × 17 = 476
23 × 5 × 13 = 520
24 × 5 × 7 = 560
5 × 7 × 17 = 595
23 × 5 × 17 = 680
22 × 173 = 692
23 × 7 × 13 = 728
5 × 173 = 865
22 × 13 × 17 = 884
2 × 5 × 7 × 13 = 910
23 × 7 × 17 = 952
24 × 5 × 13 = 1,040
5 × 13 × 17 = 1,105
2 × 5 × 7 × 17 = 1,190
7 × 173 = 1,211
24 × 5 × 17 = 1,360
23 × 173 = 1,384
24 × 7 × 13 = 1,456
7 × 13 × 17 = 1,547
2 × 5 × 173 = 1,730
23 × 13 × 17 = 1,768
22 × 5 × 7 × 13 = 1,820
24 × 7 × 17 = 1,904
2 × 5 × 13 × 17 = 2,210
13 × 173 = 2,249
22 × 5 × 7 × 17 = 2,380
2 × 7 × 173 = 2,422
24 × 173 = 2,768
17 × 173 = 2,941
2 × 7 × 13 × 17 = 3,094
22 × 5 × 173 = 3,460
24 × 13 × 17 = 3,536
23 × 5 × 7 × 13 = 3,640
22 × 5 × 13 × 17 = 4,420
2 × 13 × 173 = 4,498
This list continues below...

... This list continues from above
23 × 5 × 7 × 17 = 4,760
22 × 7 × 173 = 4,844
2 × 17 × 173 = 5,882
5 × 7 × 173 = 6,055
22 × 7 × 13 × 17 = 6,188
23 × 5 × 173 = 6,920
24 × 5 × 7 × 13 = 7,280
5 × 7 × 13 × 17 = 7,735
23 × 5 × 13 × 17 = 8,840
22 × 13 × 173 = 8,996
24 × 5 × 7 × 17 = 9,520
23 × 7 × 173 = 9,688
5 × 13 × 173 = 11,245
22 × 17 × 173 = 11,764
2 × 5 × 7 × 173 = 12,110
23 × 7 × 13 × 17 = 12,376
24 × 5 × 173 = 13,840
5 × 17 × 173 = 14,705
2 × 5 × 7 × 13 × 17 = 15,470
7 × 13 × 173 = 15,743
24 × 5 × 13 × 17 = 17,680
23 × 13 × 173 = 17,992
24 × 7 × 173 = 19,376
7 × 17 × 173 = 20,587
2 × 5 × 13 × 173 = 22,490
23 × 17 × 173 = 23,528
22 × 5 × 7 × 173 = 24,220
24 × 7 × 13 × 17 = 24,752
2 × 5 × 17 × 173 = 29,410
22 × 5 × 7 × 13 × 17 = 30,940
2 × 7 × 13 × 173 = 31,486
24 × 13 × 173 = 35,984
13 × 17 × 173 = 38,233
2 × 7 × 17 × 173 = 41,174
22 × 5 × 13 × 173 = 44,980
24 × 17 × 173 = 47,056
23 × 5 × 7 × 173 = 48,440
22 × 5 × 17 × 173 = 58,820
23 × 5 × 7 × 13 × 17 = 61,880
22 × 7 × 13 × 173 = 62,972
2 × 13 × 17 × 173 = 76,466
5 × 7 × 13 × 173 = 78,715
22 × 7 × 17 × 173 = 82,348
23 × 5 × 13 × 173 = 89,960
24 × 5 × 7 × 173 = 96,880
5 × 7 × 17 × 173 = 102,935
23 × 5 × 17 × 173 = 117,640
24 × 5 × 7 × 13 × 17 = 123,760
23 × 7 × 13 × 173 = 125,944
22 × 13 × 17 × 173 = 152,932
2 × 5 × 7 × 13 × 173 = 157,430
23 × 7 × 17 × 173 = 164,696
24 × 5 × 13 × 173 = 179,920
5 × 13 × 17 × 173 = 191,165
2 × 5 × 7 × 17 × 173 = 205,870
24 × 5 × 17 × 173 = 235,280
24 × 7 × 13 × 173 = 251,888
7 × 13 × 17 × 173 = 267,631
23 × 13 × 17 × 173 = 305,864
22 × 5 × 7 × 13 × 173 = 314,860
24 × 7 × 17 × 173 = 329,392
2 × 5 × 13 × 17 × 173 = 382,330
22 × 5 × 7 × 17 × 173 = 411,740
2 × 7 × 13 × 17 × 173 = 535,262
24 × 13 × 17 × 173 = 611,728
23 × 5 × 7 × 13 × 173 = 629,720
22 × 5 × 13 × 17 × 173 = 764,660
23 × 5 × 7 × 17 × 173 = 823,480
22 × 7 × 13 × 17 × 173 = 1,070,524
24 × 5 × 7 × 13 × 173 = 1,259,440
5 × 7 × 13 × 17 × 173 = 1,338,155
23 × 5 × 13 × 17 × 173 = 1,529,320
24 × 5 × 7 × 17 × 173 = 1,646,960
23 × 7 × 13 × 17 × 173 = 2,141,048
2 × 5 × 7 × 13 × 17 × 173 = 2,676,310
24 × 5 × 13 × 17 × 173 = 3,058,640
24 × 7 × 13 × 17 × 173 = 4,282,096
22 × 5 × 7 × 13 × 17 × 173 = 5,352,620
23 × 5 × 7 × 13 × 17 × 173 = 10,705,240
24 × 5 × 7 × 13 × 17 × 173 = 21,410,480

The final answer:
(scroll down)

21,410,480 has 160 factors (divisors):
1; 2; 4; 5; 7; 8; 10; 13; 14; 16; 17; 20; 26; 28; 34; 35; 40; 52; 56; 65; 68; 70; 80; 85; 91; 104; 112; 119; 130; 136; 140; 170; 173; 182; 208; 221; 238; 260; 272; 280; 340; 346; 364; 442; 455; 476; 520; 560; 595; 680; 692; 728; 865; 884; 910; 952; 1,040; 1,105; 1,190; 1,211; 1,360; 1,384; 1,456; 1,547; 1,730; 1,768; 1,820; 1,904; 2,210; 2,249; 2,380; 2,422; 2,768; 2,941; 3,094; 3,460; 3,536; 3,640; 4,420; 4,498; 4,760; 4,844; 5,882; 6,055; 6,188; 6,920; 7,280; 7,735; 8,840; 8,996; 9,520; 9,688; 11,245; 11,764; 12,110; 12,376; 13,840; 14,705; 15,470; 15,743; 17,680; 17,992; 19,376; 20,587; 22,490; 23,528; 24,220; 24,752; 29,410; 30,940; 31,486; 35,984; 38,233; 41,174; 44,980; 47,056; 48,440; 58,820; 61,880; 62,972; 76,466; 78,715; 82,348; 89,960; 96,880; 102,935; 117,640; 123,760; 125,944; 152,932; 157,430; 164,696; 179,920; 191,165; 205,870; 235,280; 251,888; 267,631; 305,864; 314,860; 329,392; 382,330; 411,740; 535,262; 611,728; 629,720; 764,660; 823,480; 1,070,524; 1,259,440; 1,338,155; 1,529,320; 1,646,960; 2,141,048; 2,676,310; 3,058,640; 4,282,096; 5,352,620; 10,705,240 and 21,410,480
out of which 6 prime factors: 2; 5; 7; 13; 17 and 173
21,410,480 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".