Given the Number 323,136, Calculate (Find) All the Factors (All the Divisors) of the Number 323,136 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 323,136

1. Carry out the prime factorization of the number 323,136:

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


323,136 = 26 × 33 × 11 × 17
323,136 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 323,136

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
prime factor = 3
22 = 4
2 × 3 = 6
23 = 8
32 = 9
prime factor = 11
22 × 3 = 12
24 = 16
prime factor = 17
2 × 32 = 18
2 × 11 = 22
23 × 3 = 24
33 = 27
25 = 32
3 × 11 = 33
2 × 17 = 34
22 × 32 = 36
22 × 11 = 44
24 × 3 = 48
3 × 17 = 51
2 × 33 = 54
26 = 64
2 × 3 × 11 = 66
22 × 17 = 68
23 × 32 = 72
23 × 11 = 88
25 × 3 = 96
32 × 11 = 99
2 × 3 × 17 = 102
22 × 33 = 108
22 × 3 × 11 = 132
23 × 17 = 136
24 × 32 = 144
32 × 17 = 153
24 × 11 = 176
11 × 17 = 187
26 × 3 = 192
2 × 32 × 11 = 198
22 × 3 × 17 = 204
23 × 33 = 216
23 × 3 × 11 = 264
24 × 17 = 272
25 × 32 = 288
33 × 11 = 297
2 × 32 × 17 = 306
25 × 11 = 352
2 × 11 × 17 = 374
22 × 32 × 11 = 396
23 × 3 × 17 = 408
24 × 33 = 432
33 × 17 = 459
24 × 3 × 11 = 528
25 × 17 = 544
3 × 11 × 17 = 561
This list continues below...

... This list continues from above
26 × 32 = 576
2 × 33 × 11 = 594
22 × 32 × 17 = 612
26 × 11 = 704
22 × 11 × 17 = 748
23 × 32 × 11 = 792
24 × 3 × 17 = 816
25 × 33 = 864
2 × 33 × 17 = 918
25 × 3 × 11 = 1,056
26 × 17 = 1,088
2 × 3 × 11 × 17 = 1,122
22 × 33 × 11 = 1,188
23 × 32 × 17 = 1,224
23 × 11 × 17 = 1,496
24 × 32 × 11 = 1,584
25 × 3 × 17 = 1,632
32 × 11 × 17 = 1,683
26 × 33 = 1,728
22 × 33 × 17 = 1,836
26 × 3 × 11 = 2,112
22 × 3 × 11 × 17 = 2,244
23 × 33 × 11 = 2,376
24 × 32 × 17 = 2,448
24 × 11 × 17 = 2,992
25 × 32 × 11 = 3,168
26 × 3 × 17 = 3,264
2 × 32 × 11 × 17 = 3,366
23 × 33 × 17 = 3,672
23 × 3 × 11 × 17 = 4,488
24 × 33 × 11 = 4,752
25 × 32 × 17 = 4,896
33 × 11 × 17 = 5,049
25 × 11 × 17 = 5,984
26 × 32 × 11 = 6,336
22 × 32 × 11 × 17 = 6,732
24 × 33 × 17 = 7,344
24 × 3 × 11 × 17 = 8,976
25 × 33 × 11 = 9,504
26 × 32 × 17 = 9,792
2 × 33 × 11 × 17 = 10,098
26 × 11 × 17 = 11,968
23 × 32 × 11 × 17 = 13,464
25 × 33 × 17 = 14,688
25 × 3 × 11 × 17 = 17,952
26 × 33 × 11 = 19,008
22 × 33 × 11 × 17 = 20,196
24 × 32 × 11 × 17 = 26,928
26 × 33 × 17 = 29,376
26 × 3 × 11 × 17 = 35,904
23 × 33 × 11 × 17 = 40,392
25 × 32 × 11 × 17 = 53,856
24 × 33 × 11 × 17 = 80,784
26 × 32 × 11 × 17 = 107,712
25 × 33 × 11 × 17 = 161,568
26 × 33 × 11 × 17 = 323,136

The final answer:
(scroll down)

323,136 has 112 factors (divisors):
1; 2; 3; 4; 6; 8; 9; 11; 12; 16; 17; 18; 22; 24; 27; 32; 33; 34; 36; 44; 48; 51; 54; 64; 66; 68; 72; 88; 96; 99; 102; 108; 132; 136; 144; 153; 176; 187; 192; 198; 204; 216; 264; 272; 288; 297; 306; 352; 374; 396; 408; 432; 459; 528; 544; 561; 576; 594; 612; 704; 748; 792; 816; 864; 918; 1,056; 1,088; 1,122; 1,188; 1,224; 1,496; 1,584; 1,632; 1,683; 1,728; 1,836; 2,112; 2,244; 2,376; 2,448; 2,992; 3,168; 3,264; 3,366; 3,672; 4,488; 4,752; 4,896; 5,049; 5,984; 6,336; 6,732; 7,344; 8,976; 9,504; 9,792; 10,098; 11,968; 13,464; 14,688; 17,952; 19,008; 20,196; 26,928; 29,376; 35,904; 40,392; 53,856; 80,784; 107,712; 161,568 and 323,136
out of which 4 prime factors: 2; 3; 11 and 17
323,136 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.

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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".