Given the Number 24,999,975 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 24,999,975

1. Carry out the prime factorization of the number 24,999,975:

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


24,999,975 = 33 × 52 × 7 × 11 × 13 × 37
24,999,975 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 24,999,975

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 = 3
prime factor = 5
prime factor = 7
32 = 9
prime factor = 11
prime factor = 13
3 × 5 = 15
3 × 7 = 21
52 = 25
33 = 27
3 × 11 = 33
5 × 7 = 35
prime factor = 37
3 × 13 = 39
32 × 5 = 45
5 × 11 = 55
32 × 7 = 63
5 × 13 = 65
3 × 52 = 75
7 × 11 = 77
7 × 13 = 91
32 × 11 = 99
3 × 5 × 7 = 105
3 × 37 = 111
32 × 13 = 117
33 × 5 = 135
11 × 13 = 143
3 × 5 × 11 = 165
52 × 7 = 175
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
32 × 52 = 225
3 × 7 × 11 = 231
7 × 37 = 259
3 × 7 × 13 = 273
52 × 11 = 275
33 × 11 = 297
32 × 5 × 7 = 315
52 × 13 = 325
32 × 37 = 333
33 × 13 = 351
5 × 7 × 11 = 385
11 × 37 = 407
3 × 11 × 13 = 429
5 × 7 × 13 = 455
13 × 37 = 481
32 × 5 × 11 = 495
3 × 52 × 7 = 525
3 × 5 × 37 = 555
32 × 5 × 13 = 585
33 × 52 = 675
32 × 7 × 11 = 693
5 × 11 × 13 = 715
3 × 7 × 37 = 777
32 × 7 × 13 = 819
3 × 52 × 11 = 825
52 × 37 = 925
33 × 5 × 7 = 945
3 × 52 × 13 = 975
33 × 37 = 999
7 × 11 × 13 = 1,001
3 × 5 × 7 × 11 = 1,155
3 × 11 × 37 = 1,221
32 × 11 × 13 = 1,287
5 × 7 × 37 = 1,295
3 × 5 × 7 × 13 = 1,365
3 × 13 × 37 = 1,443
33 × 5 × 11 = 1,485
32 × 52 × 7 = 1,575
32 × 5 × 37 = 1,665
33 × 5 × 13 = 1,755
52 × 7 × 11 = 1,925
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
3 × 5 × 11 × 13 = 2,145
52 × 7 × 13 = 2,275
32 × 7 × 37 = 2,331
5 × 13 × 37 = 2,405
33 × 7 × 13 = 2,457
32 × 52 × 11 = 2,475
3 × 52 × 37 = 2,775
7 × 11 × 37 = 2,849
32 × 52 × 13 = 2,925
3 × 7 × 11 × 13 = 3,003
7 × 13 × 37 = 3,367
32 × 5 × 7 × 11 = 3,465
52 × 11 × 13 = 3,575
32 × 11 × 37 = 3,663
33 × 11 × 13 = 3,861
3 × 5 × 7 × 37 = 3,885
32 × 5 × 7 × 13 = 4,095
32 × 13 × 37 = 4,329
33 × 52 × 7 = 4,725
33 × 5 × 37 = 4,995
This list continues below...

... This list continues from above
5 × 7 × 11 × 13 = 5,005
11 × 13 × 37 = 5,291
3 × 52 × 7 × 11 = 5,775
3 × 5 × 11 × 37 = 6,105
32 × 5 × 11 × 13 = 6,435
52 × 7 × 37 = 6,475
3 × 52 × 7 × 13 = 6,825
33 × 7 × 37 = 6,993
3 × 5 × 13 × 37 = 7,215
33 × 52 × 11 = 7,425
32 × 52 × 37 = 8,325
3 × 7 × 11 × 37 = 8,547
33 × 52 × 13 = 8,775
32 × 7 × 11 × 13 = 9,009
3 × 7 × 13 × 37 = 10,101
52 × 11 × 37 = 10,175
33 × 5 × 7 × 11 = 10,395
3 × 52 × 11 × 13 = 10,725
33 × 11 × 37 = 10,989
32 × 5 × 7 × 37 = 11,655
52 × 13 × 37 = 12,025
33 × 5 × 7 × 13 = 12,285
33 × 13 × 37 = 12,987
5 × 7 × 11 × 37 = 14,245
3 × 5 × 7 × 11 × 13 = 15,015
3 × 11 × 13 × 37 = 15,873
5 × 7 × 13 × 37 = 16,835
32 × 52 × 7 × 11 = 17,325
32 × 5 × 11 × 37 = 18,315
33 × 5 × 11 × 13 = 19,305
3 × 52 × 7 × 37 = 19,425
32 × 52 × 7 × 13 = 20,475
32 × 5 × 13 × 37 = 21,645
33 × 52 × 37 = 24,975
52 × 7 × 11 × 13 = 25,025
32 × 7 × 11 × 37 = 25,641
5 × 11 × 13 × 37 = 26,455
33 × 7 × 11 × 13 = 27,027
32 × 7 × 13 × 37 = 30,303
3 × 52 × 11 × 37 = 30,525
32 × 52 × 11 × 13 = 32,175
33 × 5 × 7 × 37 = 34,965
3 × 52 × 13 × 37 = 36,075
7 × 11 × 13 × 37 = 37,037
3 × 5 × 7 × 11 × 37 = 42,735
32 × 5 × 7 × 11 × 13 = 45,045
32 × 11 × 13 × 37 = 47,619
3 × 5 × 7 × 13 × 37 = 50,505
33 × 52 × 7 × 11 = 51,975
33 × 5 × 11 × 37 = 54,945
32 × 52 × 7 × 37 = 58,275
33 × 52 × 7 × 13 = 61,425
33 × 5 × 13 × 37 = 64,935
52 × 7 × 11 × 37 = 71,225
3 × 52 × 7 × 11 × 13 = 75,075
33 × 7 × 11 × 37 = 76,923
3 × 5 × 11 × 13 × 37 = 79,365
52 × 7 × 13 × 37 = 84,175
33 × 7 × 13 × 37 = 90,909
32 × 52 × 11 × 37 = 91,575
33 × 52 × 11 × 13 = 96,525
32 × 52 × 13 × 37 = 108,225
3 × 7 × 11 × 13 × 37 = 111,111
32 × 5 × 7 × 11 × 37 = 128,205
52 × 11 × 13 × 37 = 132,275
33 × 5 × 7 × 11 × 13 = 135,135
33 × 11 × 13 × 37 = 142,857
32 × 5 × 7 × 13 × 37 = 151,515
33 × 52 × 7 × 37 = 174,825
5 × 7 × 11 × 13 × 37 = 185,185
3 × 52 × 7 × 11 × 37 = 213,675
32 × 52 × 7 × 11 × 13 = 225,225
32 × 5 × 11 × 13 × 37 = 238,095
3 × 52 × 7 × 13 × 37 = 252,525
33 × 52 × 11 × 37 = 274,725
33 × 52 × 13 × 37 = 324,675
32 × 7 × 11 × 13 × 37 = 333,333
33 × 5 × 7 × 11 × 37 = 384,615
3 × 52 × 11 × 13 × 37 = 396,825
33 × 5 × 7 × 13 × 37 = 454,545
3 × 5 × 7 × 11 × 13 × 37 = 555,555
32 × 52 × 7 × 11 × 37 = 641,025
33 × 52 × 7 × 11 × 13 = 675,675
33 × 5 × 11 × 13 × 37 = 714,285
32 × 52 × 7 × 13 × 37 = 757,575
52 × 7 × 11 × 13 × 37 = 925,925
33 × 7 × 11 × 13 × 37 = 999,999
32 × 52 × 11 × 13 × 37 = 1,190,475
32 × 5 × 7 × 11 × 13 × 37 = 1,666,665
33 × 52 × 7 × 11 × 37 = 1,923,075
33 × 52 × 7 × 13 × 37 = 2,272,725
3 × 52 × 7 × 11 × 13 × 37 = 2,777,775
33 × 52 × 11 × 13 × 37 = 3,571,425
33 × 5 × 7 × 11 × 13 × 37 = 4,999,995
32 × 52 × 7 × 11 × 13 × 37 = 8,333,325
33 × 52 × 7 × 11 × 13 × 37 = 24,999,975

The final answer:
(scroll down)

24,999,975 has 192 factors (divisors):
1; 3; 5; 7; 9; 11; 13; 15; 21; 25; 27; 33; 35; 37; 39; 45; 55; 63; 65; 75; 77; 91; 99; 105; 111; 117; 135; 143; 165; 175; 185; 189; 195; 225; 231; 259; 273; 275; 297; 315; 325; 333; 351; 385; 407; 429; 455; 481; 495; 525; 555; 585; 675; 693; 715; 777; 819; 825; 925; 945; 975; 999; 1,001; 1,155; 1,221; 1,287; 1,295; 1,365; 1,443; 1,485; 1,575; 1,665; 1,755; 1,925; 2,035; 2,079; 2,145; 2,275; 2,331; 2,405; 2,457; 2,475; 2,775; 2,849; 2,925; 3,003; 3,367; 3,465; 3,575; 3,663; 3,861; 3,885; 4,095; 4,329; 4,725; 4,995; 5,005; 5,291; 5,775; 6,105; 6,435; 6,475; 6,825; 6,993; 7,215; 7,425; 8,325; 8,547; 8,775; 9,009; 10,101; 10,175; 10,395; 10,725; 10,989; 11,655; 12,025; 12,285; 12,987; 14,245; 15,015; 15,873; 16,835; 17,325; 18,315; 19,305; 19,425; 20,475; 21,645; 24,975; 25,025; 25,641; 26,455; 27,027; 30,303; 30,525; 32,175; 34,965; 36,075; 37,037; 42,735; 45,045; 47,619; 50,505; 51,975; 54,945; 58,275; 61,425; 64,935; 71,225; 75,075; 76,923; 79,365; 84,175; 90,909; 91,575; 96,525; 108,225; 111,111; 128,205; 132,275; 135,135; 142,857; 151,515; 174,825; 185,185; 213,675; 225,225; 238,095; 252,525; 274,725; 324,675; 333,333; 384,615; 396,825; 454,545; 555,555; 641,025; 675,675; 714,285; 757,575; 925,925; 999,999; 1,190,475; 1,666,665; 1,923,075; 2,272,725; 2,777,775; 3,571,425; 4,999,995; 8,333,325 and 24,999,975
out of which 6 prime factors: 3; 5; 7; 11; 13 and 37
24,999,975 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".