Given the Number 48,009,024, Calculate (Find) All the Factors (All the Divisors) of the Number 48,009,024 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 48,009,024

1. Carry out the prime factorization of the number 48,009,024:

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

48,009,024 = 26 × 37 × 73
48,009,024 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 48,009,024

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
2 × 7 = 14
24 = 16
2 × 32 = 18
3 × 7 = 21
23 × 3 = 24
33 = 27
22 × 7 = 28
25 = 32
22 × 32 = 36
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
2 × 33 = 54
23 × 7 = 56
32 × 7 = 63
26 = 64
23 × 32 = 72
34 = 81
22 × 3 × 7 = 84
25 × 3 = 96
2 × 72 = 98
22 × 33 = 108
24 × 7 = 112
2 × 32 × 7 = 126
24 × 32 = 144
3 × 72 = 147
2 × 34 = 162
23 × 3 × 7 = 168
33 × 7 = 189
26 × 3 = 192
22 × 72 = 196
23 × 33 = 216
25 × 7 = 224
35 = 243
22 × 32 × 7 = 252
25 × 32 = 288
2 × 3 × 72 = 294
22 × 34 = 324
24 × 3 × 7 = 336
73 = 343
2 × 33 × 7 = 378
23 × 72 = 392
24 × 33 = 432
32 × 72 = 441
26 × 7 = 448
2 × 35 = 486
23 × 32 × 7 = 504
34 × 7 = 567
26 × 32 = 576
22 × 3 × 72 = 588
23 × 34 = 648
25 × 3 × 7 = 672
2 × 73 = 686
36 = 729
22 × 33 × 7 = 756
24 × 72 = 784
25 × 33 = 864
2 × 32 × 72 = 882
22 × 35 = 972
24 × 32 × 7 = 1,008
3 × 73 = 1,029
2 × 34 × 7 = 1,134
23 × 3 × 72 = 1,176
24 × 34 = 1,296
33 × 72 = 1,323
26 × 3 × 7 = 1,344
22 × 73 = 1,372
2 × 36 = 1,458
23 × 33 × 7 = 1,512
25 × 72 = 1,568
35 × 7 = 1,701
26 × 33 = 1,728
22 × 32 × 72 = 1,764
23 × 35 = 1,944
25 × 32 × 7 = 2,016
2 × 3 × 73 = 2,058
37 = 2,187
22 × 34 × 7 = 2,268
24 × 3 × 72 = 2,352
25 × 34 = 2,592
2 × 33 × 72 = 2,646
23 × 73 = 2,744
22 × 36 = 2,916
24 × 33 × 7 = 3,024
32 × 73 = 3,087
26 × 72 = 3,136
2 × 35 × 7 = 3,402
23 × 32 × 72 = 3,528
24 × 35 = 3,888
34 × 72 = 3,969
26 × 32 × 7 = 4,032
22 × 3 × 73 = 4,116
2 × 37 = 4,374
23 × 34 × 7 = 4,536
25 × 3 × 72 = 4,704
36 × 7 = 5,103
26 × 34 = 5,184
22 × 33 × 72 = 5,292
24 × 73 = 5,488
23 × 36 = 5,832
25 × 33 × 7 = 6,048
2 × 32 × 73 = 6,174
22 × 35 × 7 = 6,804
This list continues below...

... This list continues from above
24 × 32 × 72 = 7,056
25 × 35 = 7,776
2 × 34 × 72 = 7,938
23 × 3 × 73 = 8,232
22 × 37 = 8,748
24 × 34 × 7 = 9,072
33 × 73 = 9,261
26 × 3 × 72 = 9,408
2 × 36 × 7 = 10,206
23 × 33 × 72 = 10,584
25 × 73 = 10,976
24 × 36 = 11,664
35 × 72 = 11,907
26 × 33 × 7 = 12,096
22 × 32 × 73 = 12,348
23 × 35 × 7 = 13,608
25 × 32 × 72 = 14,112
37 × 7 = 15,309
26 × 35 = 15,552
22 × 34 × 72 = 15,876
24 × 3 × 73 = 16,464
23 × 37 = 17,496
25 × 34 × 7 = 18,144
2 × 33 × 73 = 18,522
22 × 36 × 7 = 20,412
24 × 33 × 72 = 21,168
26 × 73 = 21,952
25 × 36 = 23,328
2 × 35 × 72 = 23,814
23 × 32 × 73 = 24,696
24 × 35 × 7 = 27,216
34 × 73 = 27,783
26 × 32 × 72 = 28,224
2 × 37 × 7 = 30,618
23 × 34 × 72 = 31,752
25 × 3 × 73 = 32,928
24 × 37 = 34,992
36 × 72 = 35,721
26 × 34 × 7 = 36,288
22 × 33 × 73 = 37,044
23 × 36 × 7 = 40,824
25 × 33 × 72 = 42,336
26 × 36 = 46,656
22 × 35 × 72 = 47,628
24 × 32 × 73 = 49,392
25 × 35 × 7 = 54,432
2 × 34 × 73 = 55,566
22 × 37 × 7 = 61,236
24 × 34 × 72 = 63,504
26 × 3 × 73 = 65,856
25 × 37 = 69,984
2 × 36 × 72 = 71,442
23 × 33 × 73 = 74,088
24 × 36 × 7 = 81,648
35 × 73 = 83,349
26 × 33 × 72 = 84,672
23 × 35 × 72 = 95,256
25 × 32 × 73 = 98,784
37 × 72 = 107,163
26 × 35 × 7 = 108,864
22 × 34 × 73 = 111,132
23 × 37 × 7 = 122,472
25 × 34 × 72 = 127,008
26 × 37 = 139,968
22 × 36 × 72 = 142,884
24 × 33 × 73 = 148,176
25 × 36 × 7 = 163,296
2 × 35 × 73 = 166,698
24 × 35 × 72 = 190,512
26 × 32 × 73 = 197,568
2 × 37 × 72 = 214,326
23 × 34 × 73 = 222,264
24 × 37 × 7 = 244,944
36 × 73 = 250,047
26 × 34 × 72 = 254,016
23 × 36 × 72 = 285,768
25 × 33 × 73 = 296,352
26 × 36 × 7 = 326,592
22 × 35 × 73 = 333,396
25 × 35 × 72 = 381,024
22 × 37 × 72 = 428,652
24 × 34 × 73 = 444,528
25 × 37 × 7 = 489,888
2 × 36 × 73 = 500,094
24 × 36 × 72 = 571,536
26 × 33 × 73 = 592,704
23 × 35 × 73 = 666,792
37 × 73 = 750,141
26 × 35 × 72 = 762,048
23 × 37 × 72 = 857,304
25 × 34 × 73 = 889,056
26 × 37 × 7 = 979,776
22 × 36 × 73 = 1,000,188
25 × 36 × 72 = 1,143,072
24 × 35 × 73 = 1,333,584
2 × 37 × 73 = 1,500,282
24 × 37 × 72 = 1,714,608
26 × 34 × 73 = 1,778,112
23 × 36 × 73 = 2,000,376
26 × 36 × 72 = 2,286,144
25 × 35 × 73 = 2,667,168
22 × 37 × 73 = 3,000,564
25 × 37 × 72 = 3,429,216
24 × 36 × 73 = 4,000,752
26 × 35 × 73 = 5,334,336
23 × 37 × 73 = 6,001,128
26 × 37 × 72 = 6,858,432
25 × 36 × 73 = 8,001,504
24 × 37 × 73 = 12,002,256
26 × 36 × 73 = 16,003,008
25 × 37 × 73 = 24,004,512
26 × 37 × 73 = 48,009,024

The final answer:
(scroll down)

48,009,024 has 224 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 12; 14; 16; 18; 21; 24; 27; 28; 32; 36; 42; 48; 49; 54; 56; 63; 64; 72; 81; 84; 96; 98; 108; 112; 126; 144; 147; 162; 168; 189; 192; 196; 216; 224; 243; 252; 288; 294; 324; 336; 343; 378; 392; 432; 441; 448; 486; 504; 567; 576; 588; 648; 672; 686; 729; 756; 784; 864; 882; 972; 1,008; 1,029; 1,134; 1,176; 1,296; 1,323; 1,344; 1,372; 1,458; 1,512; 1,568; 1,701; 1,728; 1,764; 1,944; 2,016; 2,058; 2,187; 2,268; 2,352; 2,592; 2,646; 2,744; 2,916; 3,024; 3,087; 3,136; 3,402; 3,528; 3,888; 3,969; 4,032; 4,116; 4,374; 4,536; 4,704; 5,103; 5,184; 5,292; 5,488; 5,832; 6,048; 6,174; 6,804; 7,056; 7,776; 7,938; 8,232; 8,748; 9,072; 9,261; 9,408; 10,206; 10,584; 10,976; 11,664; 11,907; 12,096; 12,348; 13,608; 14,112; 15,309; 15,552; 15,876; 16,464; 17,496; 18,144; 18,522; 20,412; 21,168; 21,952; 23,328; 23,814; 24,696; 27,216; 27,783; 28,224; 30,618; 31,752; 32,928; 34,992; 35,721; 36,288; 37,044; 40,824; 42,336; 46,656; 47,628; 49,392; 54,432; 55,566; 61,236; 63,504; 65,856; 69,984; 71,442; 74,088; 81,648; 83,349; 84,672; 95,256; 98,784; 107,163; 108,864; 111,132; 122,472; 127,008; 139,968; 142,884; 148,176; 163,296; 166,698; 190,512; 197,568; 214,326; 222,264; 244,944; 250,047; 254,016; 285,768; 296,352; 326,592; 333,396; 381,024; 428,652; 444,528; 489,888; 500,094; 571,536; 592,704; 666,792; 750,141; 762,048; 857,304; 889,056; 979,776; 1,000,188; 1,143,072; 1,333,584; 1,500,282; 1,714,608; 1,778,112; 2,000,376; 2,286,144; 2,667,168; 3,000,564; 3,429,216; 4,000,752; 5,334,336; 6,001,128; 6,858,432; 8,001,504; 12,002,256; 16,003,008; 24,004,512 and 48,009,024
out of which 3 prime factors: 2; 3 and 7
48,009,024 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 48,009,009?

» What are all the proper, improper and prime factors (divisors) of the number 48,009,032?


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".