Given the Number 3,985,072, Calculate (Find) All the Factors (All the Divisors) of the Number 3,985,072 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 3,985,072

1. Carry out the prime factorization of the number 3,985,072:

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

3,985,072 = 24 × 72 × 13 × 17 × 23
3,985,072 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* 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 3,985,072

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 = 7
23 = 8
prime factor = 13
2 × 7 = 14
24 = 16
prime factor = 17
prime factor = 23
2 × 13 = 26
22 × 7 = 28
2 × 17 = 34
2 × 23 = 46
72 = 49
22 × 13 = 52
23 × 7 = 56
22 × 17 = 68
7 × 13 = 91
22 × 23 = 92
2 × 72 = 98
23 × 13 = 104
24 × 7 = 112
7 × 17 = 119
23 × 17 = 136
7 × 23 = 161
2 × 7 × 13 = 182
23 × 23 = 184
22 × 72 = 196
24 × 13 = 208
13 × 17 = 221
2 × 7 × 17 = 238
24 × 17 = 272
13 × 23 = 299
2 × 7 × 23 = 322
22 × 7 × 13 = 364
24 × 23 = 368
17 × 23 = 391
23 × 72 = 392
2 × 13 × 17 = 442
22 × 7 × 17 = 476
2 × 13 × 23 = 598
72 × 13 = 637
22 × 7 × 23 = 644
23 × 7 × 13 = 728
2 × 17 × 23 = 782
24 × 72 = 784
72 × 17 = 833
22 × 13 × 17 = 884
23 × 7 × 17 = 952
72 × 23 = 1,127
22 × 13 × 23 = 1,196
2 × 72 × 13 = 1,274
23 × 7 × 23 = 1,288
24 × 7 × 13 = 1,456
7 × 13 × 17 = 1,547
22 × 17 × 23 = 1,564
2 × 72 × 17 = 1,666
23 × 13 × 17 = 1,768
24 × 7 × 17 = 1,904
This list continues below...

... This list continues from above
7 × 13 × 23 = 2,093
2 × 72 × 23 = 2,254
23 × 13 × 23 = 2,392
22 × 72 × 13 = 2,548
24 × 7 × 23 = 2,576
7 × 17 × 23 = 2,737
2 × 7 × 13 × 17 = 3,094
23 × 17 × 23 = 3,128
22 × 72 × 17 = 3,332
24 × 13 × 17 = 3,536
2 × 7 × 13 × 23 = 4,186
22 × 72 × 23 = 4,508
24 × 13 × 23 = 4,784
13 × 17 × 23 = 5,083
23 × 72 × 13 = 5,096
2 × 7 × 17 × 23 = 5,474
22 × 7 × 13 × 17 = 6,188
24 × 17 × 23 = 6,256
23 × 72 × 17 = 6,664
22 × 7 × 13 × 23 = 8,372
23 × 72 × 23 = 9,016
2 × 13 × 17 × 23 = 10,166
24 × 72 × 13 = 10,192
72 × 13 × 17 = 10,829
22 × 7 × 17 × 23 = 10,948
23 × 7 × 13 × 17 = 12,376
24 × 72 × 17 = 13,328
72 × 13 × 23 = 14,651
23 × 7 × 13 × 23 = 16,744
24 × 72 × 23 = 18,032
72 × 17 × 23 = 19,159
22 × 13 × 17 × 23 = 20,332
2 × 72 × 13 × 17 = 21,658
23 × 7 × 17 × 23 = 21,896
24 × 7 × 13 × 17 = 24,752
2 × 72 × 13 × 23 = 29,302
24 × 7 × 13 × 23 = 33,488
7 × 13 × 17 × 23 = 35,581
2 × 72 × 17 × 23 = 38,318
23 × 13 × 17 × 23 = 40,664
22 × 72 × 13 × 17 = 43,316
24 × 7 × 17 × 23 = 43,792
22 × 72 × 13 × 23 = 58,604
2 × 7 × 13 × 17 × 23 = 71,162
22 × 72 × 17 × 23 = 76,636
24 × 13 × 17 × 23 = 81,328
23 × 72 × 13 × 17 = 86,632
23 × 72 × 13 × 23 = 117,208
22 × 7 × 13 × 17 × 23 = 142,324
23 × 72 × 17 × 23 = 153,272
24 × 72 × 13 × 17 = 173,264
24 × 72 × 13 × 23 = 234,416
72 × 13 × 17 × 23 = 249,067
23 × 7 × 13 × 17 × 23 = 284,648
24 × 72 × 17 × 23 = 306,544
2 × 72 × 13 × 17 × 23 = 498,134
24 × 7 × 13 × 17 × 23 = 569,296
22 × 72 × 13 × 17 × 23 = 996,268
23 × 72 × 13 × 17 × 23 = 1,992,536
24 × 72 × 13 × 17 × 23 = 3,985,072

The final answer:
(scroll down)

3,985,072 has 120 factors (divisors):
1; 2; 4; 7; 8; 13; 14; 16; 17; 23; 26; 28; 34; 46; 49; 52; 56; 68; 91; 92; 98; 104; 112; 119; 136; 161; 182; 184; 196; 208; 221; 238; 272; 299; 322; 364; 368; 391; 392; 442; 476; 598; 637; 644; 728; 782; 784; 833; 884; 952; 1,127; 1,196; 1,274; 1,288; 1,456; 1,547; 1,564; 1,666; 1,768; 1,904; 2,093; 2,254; 2,392; 2,548; 2,576; 2,737; 3,094; 3,128; 3,332; 3,536; 4,186; 4,508; 4,784; 5,083; 5,096; 5,474; 6,188; 6,256; 6,664; 8,372; 9,016; 10,166; 10,192; 10,829; 10,948; 12,376; 13,328; 14,651; 16,744; 18,032; 19,159; 20,332; 21,658; 21,896; 24,752; 29,302; 33,488; 35,581; 38,318; 40,664; 43,316; 43,792; 58,604; 71,162; 76,636; 81,328; 86,632; 117,208; 142,324; 153,272; 173,264; 234,416; 249,067; 284,648; 306,544; 498,134; 569,296; 996,268; 1,992,536 and 3,985,072
out of which 5 prime factors: 2; 7; 13; 17 and 23
3,985,072 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.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 3,985,067?

» What are all the proper, improper and prime factors (divisors) of the number 3,985,082?


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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The list of all the calculated factors (divisors) of one or two numbers

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".