Given the Number 4,429,152, Calculate (Find) All the Factors (All the Divisors) of the Number 4,429,152 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 4,429,152

1. Carry out the prime factorization of the number 4,429,152:

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


4,429,152 = 25 × 32 × 7 × 133
4,429,152 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 4,429,152

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
prime factor = 7
23 = 8
32 = 9
22 × 3 = 12
prime factor = 13
2 × 7 = 14
24 = 16
2 × 32 = 18
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
22 × 7 = 28
25 = 32
22 × 32 = 36
3 × 13 = 39
2 × 3 × 7 = 42
24 × 3 = 48
22 × 13 = 52
23 × 7 = 56
32 × 7 = 63
23 × 32 = 72
2 × 3 × 13 = 78
22 × 3 × 7 = 84
7 × 13 = 91
25 × 3 = 96
23 × 13 = 104
24 × 7 = 112
32 × 13 = 117
2 × 32 × 7 = 126
24 × 32 = 144
22 × 3 × 13 = 156
23 × 3 × 7 = 168
132 = 169
2 × 7 × 13 = 182
24 × 13 = 208
25 × 7 = 224
2 × 32 × 13 = 234
22 × 32 × 7 = 252
3 × 7 × 13 = 273
25 × 32 = 288
23 × 3 × 13 = 312
24 × 3 × 7 = 336
2 × 132 = 338
22 × 7 × 13 = 364
25 × 13 = 416
22 × 32 × 13 = 468
23 × 32 × 7 = 504
3 × 132 = 507
2 × 3 × 7 × 13 = 546
24 × 3 × 13 = 624
25 × 3 × 7 = 672
22 × 132 = 676
23 × 7 × 13 = 728
32 × 7 × 13 = 819
23 × 32 × 13 = 936
24 × 32 × 7 = 1,008
2 × 3 × 132 = 1,014
22 × 3 × 7 × 13 = 1,092
7 × 132 = 1,183
25 × 3 × 13 = 1,248
23 × 132 = 1,352
24 × 7 × 13 = 1,456
32 × 132 = 1,521
2 × 32 × 7 × 13 = 1,638
24 × 32 × 13 = 1,872
25 × 32 × 7 = 2,016
22 × 3 × 132 = 2,028
This list continues below...

... This list continues from above
23 × 3 × 7 × 13 = 2,184
133 = 2,197
2 × 7 × 132 = 2,366
24 × 132 = 2,704
25 × 7 × 13 = 2,912
2 × 32 × 132 = 3,042
22 × 32 × 7 × 13 = 3,276
3 × 7 × 132 = 3,549
25 × 32 × 13 = 3,744
23 × 3 × 132 = 4,056
24 × 3 × 7 × 13 = 4,368
2 × 133 = 4,394
22 × 7 × 132 = 4,732
25 × 132 = 5,408
22 × 32 × 132 = 6,084
23 × 32 × 7 × 13 = 6,552
3 × 133 = 6,591
2 × 3 × 7 × 132 = 7,098
24 × 3 × 132 = 8,112
25 × 3 × 7 × 13 = 8,736
22 × 133 = 8,788
23 × 7 × 132 = 9,464
32 × 7 × 132 = 10,647
23 × 32 × 132 = 12,168
24 × 32 × 7 × 13 = 13,104
2 × 3 × 133 = 13,182
22 × 3 × 7 × 132 = 14,196
7 × 133 = 15,379
25 × 3 × 132 = 16,224
23 × 133 = 17,576
24 × 7 × 132 = 18,928
32 × 133 = 19,773
2 × 32 × 7 × 132 = 21,294
24 × 32 × 132 = 24,336
25 × 32 × 7 × 13 = 26,208
22 × 3 × 133 = 26,364
23 × 3 × 7 × 132 = 28,392
2 × 7 × 133 = 30,758
24 × 133 = 35,152
25 × 7 × 132 = 37,856
2 × 32 × 133 = 39,546
22 × 32 × 7 × 132 = 42,588
3 × 7 × 133 = 46,137
25 × 32 × 132 = 48,672
23 × 3 × 133 = 52,728
24 × 3 × 7 × 132 = 56,784
22 × 7 × 133 = 61,516
25 × 133 = 70,304
22 × 32 × 133 = 79,092
23 × 32 × 7 × 132 = 85,176
2 × 3 × 7 × 133 = 92,274
24 × 3 × 133 = 105,456
25 × 3 × 7 × 132 = 113,568
23 × 7 × 133 = 123,032
32 × 7 × 133 = 138,411
23 × 32 × 133 = 158,184
24 × 32 × 7 × 132 = 170,352
22 × 3 × 7 × 133 = 184,548
25 × 3 × 133 = 210,912
24 × 7 × 133 = 246,064
2 × 32 × 7 × 133 = 276,822
24 × 32 × 133 = 316,368
25 × 32 × 7 × 132 = 340,704
23 × 3 × 7 × 133 = 369,096
25 × 7 × 133 = 492,128
22 × 32 × 7 × 133 = 553,644
25 × 32 × 133 = 632,736
24 × 3 × 7 × 133 = 738,192
23 × 32 × 7 × 133 = 1,107,288
25 × 3 × 7 × 133 = 1,476,384
24 × 32 × 7 × 133 = 2,214,576
25 × 32 × 7 × 133 = 4,429,152

The final answer:
(scroll down)

4,429,152 has 144 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 12; 13; 14; 16; 18; 21; 24; 26; 28; 32; 36; 39; 42; 48; 52; 56; 63; 72; 78; 84; 91; 96; 104; 112; 117; 126; 144; 156; 168; 169; 182; 208; 224; 234; 252; 273; 288; 312; 336; 338; 364; 416; 468; 504; 507; 546; 624; 672; 676; 728; 819; 936; 1,008; 1,014; 1,092; 1,183; 1,248; 1,352; 1,456; 1,521; 1,638; 1,872; 2,016; 2,028; 2,184; 2,197; 2,366; 2,704; 2,912; 3,042; 3,276; 3,549; 3,744; 4,056; 4,368; 4,394; 4,732; 5,408; 6,084; 6,552; 6,591; 7,098; 8,112; 8,736; 8,788; 9,464; 10,647; 12,168; 13,104; 13,182; 14,196; 15,379; 16,224; 17,576; 18,928; 19,773; 21,294; 24,336; 26,208; 26,364; 28,392; 30,758; 35,152; 37,856; 39,546; 42,588; 46,137; 48,672; 52,728; 56,784; 61,516; 70,304; 79,092; 85,176; 92,274; 105,456; 113,568; 123,032; 138,411; 158,184; 170,352; 184,548; 210,912; 246,064; 276,822; 316,368; 340,704; 369,096; 492,128; 553,644; 632,736; 738,192; 1,107,288; 1,476,384; 2,214,576 and 4,429,152
out of which 4 prime factors: 2; 3; 7 and 13
4,429,152 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

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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".