Given the Number 320,320, Calculate (Find) All the Factors (All the Divisors) of the Number 320,320 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 320,320

1. Carry out the prime factorization of the number 320,320:

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


320,320 = 26 × 5 × 7 × 11 × 13
320,320 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 320,320

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 = 11
prime factor = 13
2 × 7 = 14
24 = 16
22 × 5 = 20
2 × 11 = 22
2 × 13 = 26
22 × 7 = 28
25 = 32
5 × 7 = 35
23 × 5 = 40
22 × 11 = 44
22 × 13 = 52
5 × 11 = 55
23 × 7 = 56
26 = 64
5 × 13 = 65
2 × 5 × 7 = 70
7 × 11 = 77
24 × 5 = 80
23 × 11 = 88
7 × 13 = 91
23 × 13 = 104
2 × 5 × 11 = 110
24 × 7 = 112
2 × 5 × 13 = 130
22 × 5 × 7 = 140
11 × 13 = 143
2 × 7 × 11 = 154
25 × 5 = 160
24 × 11 = 176
2 × 7 × 13 = 182
24 × 13 = 208
22 × 5 × 11 = 220
25 × 7 = 224
22 × 5 × 13 = 260
23 × 5 × 7 = 280
2 × 11 × 13 = 286
22 × 7 × 11 = 308
26 × 5 = 320
25 × 11 = 352
22 × 7 × 13 = 364
5 × 7 × 11 = 385
25 × 13 = 416
23 × 5 × 11 = 440
26 × 7 = 448
5 × 7 × 13 = 455
23 × 5 × 13 = 520
24 × 5 × 7 = 560
This list continues below...

... This list continues from above
22 × 11 × 13 = 572
23 × 7 × 11 = 616
26 × 11 = 704
5 × 11 × 13 = 715
23 × 7 × 13 = 728
2 × 5 × 7 × 11 = 770
26 × 13 = 832
24 × 5 × 11 = 880
2 × 5 × 7 × 13 = 910
7 × 11 × 13 = 1,001
24 × 5 × 13 = 1,040
25 × 5 × 7 = 1,120
23 × 11 × 13 = 1,144
24 × 7 × 11 = 1,232
2 × 5 × 11 × 13 = 1,430
24 × 7 × 13 = 1,456
22 × 5 × 7 × 11 = 1,540
25 × 5 × 11 = 1,760
22 × 5 × 7 × 13 = 1,820
2 × 7 × 11 × 13 = 2,002
25 × 5 × 13 = 2,080
26 × 5 × 7 = 2,240
24 × 11 × 13 = 2,288
25 × 7 × 11 = 2,464
22 × 5 × 11 × 13 = 2,860
25 × 7 × 13 = 2,912
23 × 5 × 7 × 11 = 3,080
26 × 5 × 11 = 3,520
23 × 5 × 7 × 13 = 3,640
22 × 7 × 11 × 13 = 4,004
26 × 5 × 13 = 4,160
25 × 11 × 13 = 4,576
26 × 7 × 11 = 4,928
5 × 7 × 11 × 13 = 5,005
23 × 5 × 11 × 13 = 5,720
26 × 7 × 13 = 5,824
24 × 5 × 7 × 11 = 6,160
24 × 5 × 7 × 13 = 7,280
23 × 7 × 11 × 13 = 8,008
26 × 11 × 13 = 9,152
2 × 5 × 7 × 11 × 13 = 10,010
24 × 5 × 11 × 13 = 11,440
25 × 5 × 7 × 11 = 12,320
25 × 5 × 7 × 13 = 14,560
24 × 7 × 11 × 13 = 16,016
22 × 5 × 7 × 11 × 13 = 20,020
25 × 5 × 11 × 13 = 22,880
26 × 5 × 7 × 11 = 24,640
26 × 5 × 7 × 13 = 29,120
25 × 7 × 11 × 13 = 32,032
23 × 5 × 7 × 11 × 13 = 40,040
26 × 5 × 11 × 13 = 45,760
26 × 7 × 11 × 13 = 64,064
24 × 5 × 7 × 11 × 13 = 80,080
25 × 5 × 7 × 11 × 13 = 160,160
26 × 5 × 7 × 11 × 13 = 320,320

The final answer:
(scroll down)

320,320 has 112 factors (divisors):
1; 2; 4; 5; 7; 8; 10; 11; 13; 14; 16; 20; 22; 26; 28; 32; 35; 40; 44; 52; 55; 56; 64; 65; 70; 77; 80; 88; 91; 104; 110; 112; 130; 140; 143; 154; 160; 176; 182; 208; 220; 224; 260; 280; 286; 308; 320; 352; 364; 385; 416; 440; 448; 455; 520; 560; 572; 616; 704; 715; 728; 770; 832; 880; 910; 1,001; 1,040; 1,120; 1,144; 1,232; 1,430; 1,456; 1,540; 1,760; 1,820; 2,002; 2,080; 2,240; 2,288; 2,464; 2,860; 2,912; 3,080; 3,520; 3,640; 4,004; 4,160; 4,576; 4,928; 5,005; 5,720; 5,824; 6,160; 7,280; 8,008; 9,152; 10,010; 11,440; 12,320; 14,560; 16,016; 20,020; 22,880; 24,640; 29,120; 32,032; 40,040; 45,760; 64,064; 80,080; 160,160 and 320,320
out of which 5 prime factors: 2; 5; 7; 11 and 13
320,320 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.


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

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".