Given the Number 470,448, Calculate (Find) All the Factors (All the Divisors) of the Number 470,448 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 470,448

1. Carry out the prime factorization of the number 470,448:

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


470,448 = 24 × 35 × 112
470,448 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 470,448

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
2 × 32 = 18
2 × 11 = 22
23 × 3 = 24
33 = 27
3 × 11 = 33
22 × 32 = 36
22 × 11 = 44
24 × 3 = 48
2 × 33 = 54
2 × 3 × 11 = 66
23 × 32 = 72
34 = 81
23 × 11 = 88
32 × 11 = 99
22 × 33 = 108
112 = 121
22 × 3 × 11 = 132
24 × 32 = 144
2 × 34 = 162
24 × 11 = 176
2 × 32 × 11 = 198
23 × 33 = 216
2 × 112 = 242
35 = 243
23 × 3 × 11 = 264
33 × 11 = 297
22 × 34 = 324
3 × 112 = 363
22 × 32 × 11 = 396
24 × 33 = 432
22 × 112 = 484
2 × 35 = 486
24 × 3 × 11 = 528
2 × 33 × 11 = 594
23 × 34 = 648
This list continues below...

... This list continues from above
2 × 3 × 112 = 726
23 × 32 × 11 = 792
34 × 11 = 891
23 × 112 = 968
22 × 35 = 972
32 × 112 = 1,089
22 × 33 × 11 = 1,188
24 × 34 = 1,296
22 × 3 × 112 = 1,452
24 × 32 × 11 = 1,584
2 × 34 × 11 = 1,782
24 × 112 = 1,936
23 × 35 = 1,944
2 × 32 × 112 = 2,178
23 × 33 × 11 = 2,376
35 × 11 = 2,673
23 × 3 × 112 = 2,904
33 × 112 = 3,267
22 × 34 × 11 = 3,564
24 × 35 = 3,888
22 × 32 × 112 = 4,356
24 × 33 × 11 = 4,752
2 × 35 × 11 = 5,346
24 × 3 × 112 = 5,808
2 × 33 × 112 = 6,534
23 × 34 × 11 = 7,128
23 × 32 × 112 = 8,712
34 × 112 = 9,801
22 × 35 × 11 = 10,692
22 × 33 × 112 = 13,068
24 × 34 × 11 = 14,256
24 × 32 × 112 = 17,424
2 × 34 × 112 = 19,602
23 × 35 × 11 = 21,384
23 × 33 × 112 = 26,136
35 × 112 = 29,403
22 × 34 × 112 = 39,204
24 × 35 × 11 = 42,768
24 × 33 × 112 = 52,272
2 × 35 × 112 = 58,806
23 × 34 × 112 = 78,408
22 × 35 × 112 = 117,612
24 × 34 × 112 = 156,816
23 × 35 × 112 = 235,224
24 × 35 × 112 = 470,448

The final answer:
(scroll down)

470,448 has 90 factors (divisors):
1; 2; 3; 4; 6; 8; 9; 11; 12; 16; 18; 22; 24; 27; 33; 36; 44; 48; 54; 66; 72; 81; 88; 99; 108; 121; 132; 144; 162; 176; 198; 216; 242; 243; 264; 297; 324; 363; 396; 432; 484; 486; 528; 594; 648; 726; 792; 891; 968; 972; 1,089; 1,188; 1,296; 1,452; 1,584; 1,782; 1,936; 1,944; 2,178; 2,376; 2,673; 2,904; 3,267; 3,564; 3,888; 4,356; 4,752; 5,346; 5,808; 6,534; 7,128; 8,712; 9,801; 10,692; 13,068; 14,256; 17,424; 19,602; 21,384; 26,136; 29,403; 39,204; 42,768; 52,272; 58,806; 78,408; 117,612; 156,816; 235,224 and 470,448
out of which 3 prime factors: 2; 3 and 11
470,448 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".