Given the Number 14,999,985 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 14,999,985

1. Carry out the prime factorization of the number 14,999,985:

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


14,999,985 = 34 × 5 × 7 × 11 × 13 × 37
14,999,985 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 14,999,985

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
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
7 × 11 = 77
34 = 81
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
5 × 37 = 185
33 × 7 = 189
3 × 5 × 13 = 195
3 × 7 × 11 = 231
7 × 37 = 259
3 × 7 × 13 = 273
33 × 11 = 297
32 × 5 × 7 = 315
32 × 37 = 333
33 × 13 = 351
5 × 7 × 11 = 385
34 × 5 = 405
11 × 37 = 407
3 × 11 × 13 = 429
5 × 7 × 13 = 455
13 × 37 = 481
32 × 5 × 11 = 495
3 × 5 × 37 = 555
34 × 7 = 567
32 × 5 × 13 = 585
32 × 7 × 11 = 693
5 × 11 × 13 = 715
3 × 7 × 37 = 777
32 × 7 × 13 = 819
34 × 11 = 891
33 × 5 × 7 = 945
33 × 37 = 999
7 × 11 × 13 = 1,001
34 × 13 = 1,053
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 × 5 × 37 = 1,665
33 × 5 × 13 = 1,755
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
3 × 5 × 11 × 13 = 2,145
32 × 7 × 37 = 2,331
5 × 13 × 37 = 2,405
33 × 7 × 13 = 2,457
34 × 5 × 7 = 2,835
7 × 11 × 37 = 2,849
34 × 37 = 2,997
3 × 7 × 11 × 13 = 3,003
7 × 13 × 37 = 3,367
32 × 5 × 7 × 11 = 3,465
32 × 11 × 37 = 3,663
33 × 11 × 13 = 3,861
This list continues below...

... This list continues from above
3 × 5 × 7 × 37 = 3,885
32 × 5 × 7 × 13 = 4,095
32 × 13 × 37 = 4,329
34 × 5 × 11 = 4,455
33 × 5 × 37 = 4,995
5 × 7 × 11 × 13 = 5,005
34 × 5 × 13 = 5,265
11 × 13 × 37 = 5,291
3 × 5 × 11 × 37 = 6,105
34 × 7 × 11 = 6,237
32 × 5 × 11 × 13 = 6,435
33 × 7 × 37 = 6,993
3 × 5 × 13 × 37 = 7,215
34 × 7 × 13 = 7,371
3 × 7 × 11 × 37 = 8,547
32 × 7 × 11 × 13 = 9,009
3 × 7 × 13 × 37 = 10,101
33 × 5 × 7 × 11 = 10,395
33 × 11 × 37 = 10,989
34 × 11 × 13 = 11,583
32 × 5 × 7 × 37 = 11,655
33 × 5 × 7 × 13 = 12,285
33 × 13 × 37 = 12,987
5 × 7 × 11 × 37 = 14,245
34 × 5 × 37 = 14,985
3 × 5 × 7 × 11 × 13 = 15,015
3 × 11 × 13 × 37 = 15,873
5 × 7 × 13 × 37 = 16,835
32 × 5 × 11 × 37 = 18,315
33 × 5 × 11 × 13 = 19,305
34 × 7 × 37 = 20,979
32 × 5 × 13 × 37 = 21,645
32 × 7 × 11 × 37 = 25,641
5 × 11 × 13 × 37 = 26,455
33 × 7 × 11 × 13 = 27,027
32 × 7 × 13 × 37 = 30,303
34 × 5 × 7 × 11 = 31,185
34 × 11 × 37 = 32,967
33 × 5 × 7 × 37 = 34,965
34 × 5 × 7 × 13 = 36,855
7 × 11 × 13 × 37 = 37,037
34 × 13 × 37 = 38,961
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 × 5 × 11 × 37 = 54,945
34 × 5 × 11 × 13 = 57,915
33 × 5 × 13 × 37 = 64,935
33 × 7 × 11 × 37 = 76,923
3 × 5 × 11 × 13 × 37 = 79,365
34 × 7 × 11 × 13 = 81,081
33 × 7 × 13 × 37 = 90,909
34 × 5 × 7 × 37 = 104,895
3 × 7 × 11 × 13 × 37 = 111,111
32 × 5 × 7 × 11 × 37 = 128,205
33 × 5 × 7 × 11 × 13 = 135,135
33 × 11 × 13 × 37 = 142,857
32 × 5 × 7 × 13 × 37 = 151,515
34 × 5 × 11 × 37 = 164,835
5 × 7 × 11 × 13 × 37 = 185,185
34 × 5 × 13 × 37 = 194,805
34 × 7 × 11 × 37 = 230,769
32 × 5 × 11 × 13 × 37 = 238,095
34 × 7 × 13 × 37 = 272,727
32 × 7 × 11 × 13 × 37 = 333,333
33 × 5 × 7 × 11 × 37 = 384,615
34 × 5 × 7 × 11 × 13 = 405,405
34 × 11 × 13 × 37 = 428,571
33 × 5 × 7 × 13 × 37 = 454,545
3 × 5 × 7 × 11 × 13 × 37 = 555,555
33 × 5 × 11 × 13 × 37 = 714,285
33 × 7 × 11 × 13 × 37 = 999,999
34 × 5 × 7 × 11 × 37 = 1,153,845
34 × 5 × 7 × 13 × 37 = 1,363,635
32 × 5 × 7 × 11 × 13 × 37 = 1,666,665
34 × 5 × 11 × 13 × 37 = 2,142,855
34 × 7 × 11 × 13 × 37 = 2,999,997
33 × 5 × 7 × 11 × 13 × 37 = 4,999,995
34 × 5 × 7 × 11 × 13 × 37 = 14,999,985

The final answer:
(scroll down)

14,999,985 has 160 factors (divisors):
1; 3; 5; 7; 9; 11; 13; 15; 21; 27; 33; 35; 37; 39; 45; 55; 63; 65; 77; 81; 91; 99; 105; 111; 117; 135; 143; 165; 185; 189; 195; 231; 259; 273; 297; 315; 333; 351; 385; 405; 407; 429; 455; 481; 495; 555; 567; 585; 693; 715; 777; 819; 891; 945; 999; 1,001; 1,053; 1,155; 1,221; 1,287; 1,295; 1,365; 1,443; 1,485; 1,665; 1,755; 2,035; 2,079; 2,145; 2,331; 2,405; 2,457; 2,835; 2,849; 2,997; 3,003; 3,367; 3,465; 3,663; 3,861; 3,885; 4,095; 4,329; 4,455; 4,995; 5,005; 5,265; 5,291; 6,105; 6,237; 6,435; 6,993; 7,215; 7,371; 8,547; 9,009; 10,101; 10,395; 10,989; 11,583; 11,655; 12,285; 12,987; 14,245; 14,985; 15,015; 15,873; 16,835; 18,315; 19,305; 20,979; 21,645; 25,641; 26,455; 27,027; 30,303; 31,185; 32,967; 34,965; 36,855; 37,037; 38,961; 42,735; 45,045; 47,619; 50,505; 54,945; 57,915; 64,935; 76,923; 79,365; 81,081; 90,909; 104,895; 111,111; 128,205; 135,135; 142,857; 151,515; 164,835; 185,185; 194,805; 230,769; 238,095; 272,727; 333,333; 384,615; 405,405; 428,571; 454,545; 555,555; 714,285; 999,999; 1,153,845; 1,363,635; 1,666,665; 2,142,855; 2,999,997; 4,999,995 and 14,999,985
out of which 6 prime factors: 3; 5; 7; 11; 13 and 37
14,999,985 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".