Given the Number 27,824,160, Calculate (Find) All the Factors (All the Divisors) of the Number 27,824,160 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 27,824,160

1. Carry out the prime factorization of the number 27,824,160:

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

27,824,160 = 25 × 3 × 5 × 73 × 132
27,824,160 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 27,824,160

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
prime factor = 5
2 × 3 = 6
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
24 = 16
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
5 × 7 = 35
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
22 × 13 = 52
23 × 7 = 56
22 × 3 × 5 = 60
5 × 13 = 65
2 × 5 × 7 = 70
2 × 3 × 13 = 78
24 × 5 = 80
22 × 3 × 7 = 84
7 × 13 = 91
25 × 3 = 96
2 × 72 = 98
23 × 13 = 104
3 × 5 × 7 = 105
24 × 7 = 112
23 × 3 × 5 = 120
2 × 5 × 13 = 130
22 × 5 × 7 = 140
3 × 72 = 147
22 × 3 × 13 = 156
25 × 5 = 160
23 × 3 × 7 = 168
132 = 169
2 × 7 × 13 = 182
3 × 5 × 13 = 195
22 × 72 = 196
24 × 13 = 208
2 × 3 × 5 × 7 = 210
25 × 7 = 224
24 × 3 × 5 = 240
5 × 72 = 245
22 × 5 × 13 = 260
3 × 7 × 13 = 273
23 × 5 × 7 = 280
2 × 3 × 72 = 294
23 × 3 × 13 = 312
24 × 3 × 7 = 336
2 × 132 = 338
73 = 343
22 × 7 × 13 = 364
2 × 3 × 5 × 13 = 390
23 × 72 = 392
25 × 13 = 416
22 × 3 × 5 × 7 = 420
5 × 7 × 13 = 455
25 × 3 × 5 = 480
2 × 5 × 72 = 490
3 × 132 = 507
23 × 5 × 13 = 520
2 × 3 × 7 × 13 = 546
24 × 5 × 7 = 560
22 × 3 × 72 = 588
24 × 3 × 13 = 624
72 × 13 = 637
25 × 3 × 7 = 672
22 × 132 = 676
2 × 73 = 686
23 × 7 × 13 = 728
3 × 5 × 72 = 735
22 × 3 × 5 × 13 = 780
24 × 72 = 784
23 × 3 × 5 × 7 = 840
5 × 132 = 845
2 × 5 × 7 × 13 = 910
22 × 5 × 72 = 980
2 × 3 × 132 = 1,014
3 × 73 = 1,029
24 × 5 × 13 = 1,040
22 × 3 × 7 × 13 = 1,092
25 × 5 × 7 = 1,120
23 × 3 × 72 = 1,176
7 × 132 = 1,183
25 × 3 × 13 = 1,248
2 × 72 × 13 = 1,274
23 × 132 = 1,352
3 × 5 × 7 × 13 = 1,365
22 × 73 = 1,372
24 × 7 × 13 = 1,456
2 × 3 × 5 × 72 = 1,470
23 × 3 × 5 × 13 = 1,560
25 × 72 = 1,568
24 × 3 × 5 × 7 = 1,680
2 × 5 × 132 = 1,690
5 × 73 = 1,715
22 × 5 × 7 × 13 = 1,820
3 × 72 × 13 = 1,911
23 × 5 × 72 = 1,960
22 × 3 × 132 = 2,028
2 × 3 × 73 = 2,058
25 × 5 × 13 = 2,080
23 × 3 × 7 × 13 = 2,184
24 × 3 × 72 = 2,352
2 × 7 × 132 = 2,366
3 × 5 × 132 = 2,535
22 × 72 × 13 = 2,548
24 × 132 = 2,704
2 × 3 × 5 × 7 × 13 = 2,730
23 × 73 = 2,744
25 × 7 × 13 = 2,912
22 × 3 × 5 × 72 = 2,940
24 × 3 × 5 × 13 = 3,120
5 × 72 × 13 = 3,185
25 × 3 × 5 × 7 = 3,360
22 × 5 × 132 = 3,380
2 × 5 × 73 = 3,430
3 × 7 × 132 = 3,549
23 × 5 × 7 × 13 = 3,640
2 × 3 × 72 × 13 = 3,822
24 × 5 × 72 = 3,920
23 × 3 × 132 = 4,056
22 × 3 × 73 = 4,116
24 × 3 × 7 × 13 = 4,368
73 × 13 = 4,459
25 × 3 × 72 = 4,704
22 × 7 × 132 = 4,732
2 × 3 × 5 × 132 = 5,070
23 × 72 × 13 = 5,096
3 × 5 × 73 = 5,145
This list continues below...

... This list continues from above
25 × 132 = 5,408
22 × 3 × 5 × 7 × 13 = 5,460
24 × 73 = 5,488
23 × 3 × 5 × 72 = 5,880
5 × 7 × 132 = 5,915
25 × 3 × 5 × 13 = 6,240
2 × 5 × 72 × 13 = 6,370
23 × 5 × 132 = 6,760
22 × 5 × 73 = 6,860
2 × 3 × 7 × 132 = 7,098
24 × 5 × 7 × 13 = 7,280
22 × 3 × 72 × 13 = 7,644
25 × 5 × 72 = 7,840
24 × 3 × 132 = 8,112
23 × 3 × 73 = 8,232
72 × 132 = 8,281
25 × 3 × 7 × 13 = 8,736
2 × 73 × 13 = 8,918
23 × 7 × 132 = 9,464
3 × 5 × 72 × 13 = 9,555
22 × 3 × 5 × 132 = 10,140
24 × 72 × 13 = 10,192
2 × 3 × 5 × 73 = 10,290
23 × 3 × 5 × 7 × 13 = 10,920
25 × 73 = 10,976
24 × 3 × 5 × 72 = 11,760
2 × 5 × 7 × 132 = 11,830
22 × 5 × 72 × 13 = 12,740
3 × 73 × 13 = 13,377
24 × 5 × 132 = 13,520
23 × 5 × 73 = 13,720
22 × 3 × 7 × 132 = 14,196
25 × 5 × 7 × 13 = 14,560
23 × 3 × 72 × 13 = 15,288
25 × 3 × 132 = 16,224
24 × 3 × 73 = 16,464
2 × 72 × 132 = 16,562
3 × 5 × 7 × 132 = 17,745
22 × 73 × 13 = 17,836
24 × 7 × 132 = 18,928
2 × 3 × 5 × 72 × 13 = 19,110
23 × 3 × 5 × 132 = 20,280
25 × 72 × 13 = 20,384
22 × 3 × 5 × 73 = 20,580
24 × 3 × 5 × 7 × 13 = 21,840
5 × 73 × 13 = 22,295
25 × 3 × 5 × 72 = 23,520
22 × 5 × 7 × 132 = 23,660
3 × 72 × 132 = 24,843
23 × 5 × 72 × 13 = 25,480
2 × 3 × 73 × 13 = 26,754
25 × 5 × 132 = 27,040
24 × 5 × 73 = 27,440
23 × 3 × 7 × 132 = 28,392
24 × 3 × 72 × 13 = 30,576
25 × 3 × 73 = 32,928
22 × 72 × 132 = 33,124
2 × 3 × 5 × 7 × 132 = 35,490
23 × 73 × 13 = 35,672
25 × 7 × 132 = 37,856
22 × 3 × 5 × 72 × 13 = 38,220
24 × 3 × 5 × 132 = 40,560
23 × 3 × 5 × 73 = 41,160
5 × 72 × 132 = 41,405
25 × 3 × 5 × 7 × 13 = 43,680
2 × 5 × 73 × 13 = 44,590
23 × 5 × 7 × 132 = 47,320
2 × 3 × 72 × 132 = 49,686
24 × 5 × 72 × 13 = 50,960
22 × 3 × 73 × 13 = 53,508
25 × 5 × 73 = 54,880
24 × 3 × 7 × 132 = 56,784
73 × 132 = 57,967
25 × 3 × 72 × 13 = 61,152
23 × 72 × 132 = 66,248
3 × 5 × 73 × 13 = 66,885
22 × 3 × 5 × 7 × 132 = 70,980
24 × 73 × 13 = 71,344
23 × 3 × 5 × 72 × 13 = 76,440
25 × 3 × 5 × 132 = 81,120
24 × 3 × 5 × 73 = 82,320
2 × 5 × 72 × 132 = 82,810
22 × 5 × 73 × 13 = 89,180
24 × 5 × 7 × 132 = 94,640
22 × 3 × 72 × 132 = 99,372
25 × 5 × 72 × 13 = 101,920
23 × 3 × 73 × 13 = 107,016
25 × 3 × 7 × 132 = 113,568
2 × 73 × 132 = 115,934
3 × 5 × 72 × 132 = 124,215
24 × 72 × 132 = 132,496
2 × 3 × 5 × 73 × 13 = 133,770
23 × 3 × 5 × 7 × 132 = 141,960
25 × 73 × 13 = 142,688
24 × 3 × 5 × 72 × 13 = 152,880
25 × 3 × 5 × 73 = 164,640
22 × 5 × 72 × 132 = 165,620
3 × 73 × 132 = 173,901
23 × 5 × 73 × 13 = 178,360
25 × 5 × 7 × 132 = 189,280
23 × 3 × 72 × 132 = 198,744
24 × 3 × 73 × 13 = 214,032
22 × 73 × 132 = 231,868
2 × 3 × 5 × 72 × 132 = 248,430
25 × 72 × 132 = 264,992
22 × 3 × 5 × 73 × 13 = 267,540
24 × 3 × 5 × 7 × 132 = 283,920
5 × 73 × 132 = 289,835
25 × 3 × 5 × 72 × 13 = 305,760
23 × 5 × 72 × 132 = 331,240
2 × 3 × 73 × 132 = 347,802
24 × 5 × 73 × 13 = 356,720
24 × 3 × 72 × 132 = 397,488
25 × 3 × 73 × 13 = 428,064
23 × 73 × 132 = 463,736
22 × 3 × 5 × 72 × 132 = 496,860
23 × 3 × 5 × 73 × 13 = 535,080
25 × 3 × 5 × 7 × 132 = 567,840
2 × 5 × 73 × 132 = 579,670
24 × 5 × 72 × 132 = 662,480
22 × 3 × 73 × 132 = 695,604
25 × 5 × 73 × 13 = 713,440
25 × 3 × 72 × 132 = 794,976
3 × 5 × 73 × 132 = 869,505
24 × 73 × 132 = 927,472
23 × 3 × 5 × 72 × 132 = 993,720
24 × 3 × 5 × 73 × 13 = 1,070,160
22 × 5 × 73 × 132 = 1,159,340
25 × 5 × 72 × 132 = 1,324,960
23 × 3 × 73 × 132 = 1,391,208
2 × 3 × 5 × 73 × 132 = 1,739,010
25 × 73 × 132 = 1,854,944
24 × 3 × 5 × 72 × 132 = 1,987,440
25 × 3 × 5 × 73 × 13 = 2,140,320
23 × 5 × 73 × 132 = 2,318,680
24 × 3 × 73 × 132 = 2,782,416
22 × 3 × 5 × 73 × 132 = 3,478,020
25 × 3 × 5 × 72 × 132 = 3,974,880
24 × 5 × 73 × 132 = 4,637,360
25 × 3 × 73 × 132 = 5,564,832
23 × 3 × 5 × 73 × 132 = 6,956,040
25 × 5 × 73 × 132 = 9,274,720
24 × 3 × 5 × 73 × 132 = 13,912,080
25 × 3 × 5 × 73 × 132 = 27,824,160

The final answer:
(scroll down)

27,824,160 has 288 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 13; 14; 15; 16; 20; 21; 24; 26; 28; 30; 32; 35; 39; 40; 42; 48; 49; 52; 56; 60; 65; 70; 78; 80; 84; 91; 96; 98; 104; 105; 112; 120; 130; 140; 147; 156; 160; 168; 169; 182; 195; 196; 208; 210; 224; 240; 245; 260; 273; 280; 294; 312; 336; 338; 343; 364; 390; 392; 416; 420; 455; 480; 490; 507; 520; 546; 560; 588; 624; 637; 672; 676; 686; 728; 735; 780; 784; 840; 845; 910; 980; 1,014; 1,029; 1,040; 1,092; 1,120; 1,176; 1,183; 1,248; 1,274; 1,352; 1,365; 1,372; 1,456; 1,470; 1,560; 1,568; 1,680; 1,690; 1,715; 1,820; 1,911; 1,960; 2,028; 2,058; 2,080; 2,184; 2,352; 2,366; 2,535; 2,548; 2,704; 2,730; 2,744; 2,912; 2,940; 3,120; 3,185; 3,360; 3,380; 3,430; 3,549; 3,640; 3,822; 3,920; 4,056; 4,116; 4,368; 4,459; 4,704; 4,732; 5,070; 5,096; 5,145; 5,408; 5,460; 5,488; 5,880; 5,915; 6,240; 6,370; 6,760; 6,860; 7,098; 7,280; 7,644; 7,840; 8,112; 8,232; 8,281; 8,736; 8,918; 9,464; 9,555; 10,140; 10,192; 10,290; 10,920; 10,976; 11,760; 11,830; 12,740; 13,377; 13,520; 13,720; 14,196; 14,560; 15,288; 16,224; 16,464; 16,562; 17,745; 17,836; 18,928; 19,110; 20,280; 20,384; 20,580; 21,840; 22,295; 23,520; 23,660; 24,843; 25,480; 26,754; 27,040; 27,440; 28,392; 30,576; 32,928; 33,124; 35,490; 35,672; 37,856; 38,220; 40,560; 41,160; 41,405; 43,680; 44,590; 47,320; 49,686; 50,960; 53,508; 54,880; 56,784; 57,967; 61,152; 66,248; 66,885; 70,980; 71,344; 76,440; 81,120; 82,320; 82,810; 89,180; 94,640; 99,372; 101,920; 107,016; 113,568; 115,934; 124,215; 132,496; 133,770; 141,960; 142,688; 152,880; 164,640; 165,620; 173,901; 178,360; 189,280; 198,744; 214,032; 231,868; 248,430; 264,992; 267,540; 283,920; 289,835; 305,760; 331,240; 347,802; 356,720; 397,488; 428,064; 463,736; 496,860; 535,080; 567,840; 579,670; 662,480; 695,604; 713,440; 794,976; 869,505; 927,472; 993,720; 1,070,160; 1,159,340; 1,324,960; 1,391,208; 1,739,010; 1,854,944; 1,987,440; 2,140,320; 2,318,680; 2,782,416; 3,478,020; 3,974,880; 4,637,360; 5,564,832; 6,956,040; 9,274,720; 13,912,080 and 27,824,160
out of which 5 prime factors: 2; 3; 5; 7 and 13
27,824,160 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 27,824,158?

» What are all the proper, improper and prime factors (divisors) of the number 27,824,167?


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".