Given the Number 876,960, Calculate (Find) All the Factors (All the Divisors) of the Number 876,960 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 876,960

1. Carry out the prime factorization of the number 876,960:

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


876,960 = 25 × 33 × 5 × 7 × 29
876,960 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 876,960

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
32 = 9
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
33 = 27
22 × 7 = 28
prime factor = 29
2 × 3 × 5 = 30
25 = 32
5 × 7 = 35
22 × 32 = 36
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
24 × 3 = 48
2 × 33 = 54
23 × 7 = 56
2 × 29 = 58
22 × 3 × 5 = 60
32 × 7 = 63
2 × 5 × 7 = 70
23 × 32 = 72
24 × 5 = 80
22 × 3 × 7 = 84
3 × 29 = 87
2 × 32 × 5 = 90
25 × 3 = 96
3 × 5 × 7 = 105
22 × 33 = 108
24 × 7 = 112
22 × 29 = 116
23 × 3 × 5 = 120
2 × 32 × 7 = 126
33 × 5 = 135
22 × 5 × 7 = 140
24 × 32 = 144
5 × 29 = 145
25 × 5 = 160
23 × 3 × 7 = 168
2 × 3 × 29 = 174
22 × 32 × 5 = 180
33 × 7 = 189
7 × 29 = 203
2 × 3 × 5 × 7 = 210
23 × 33 = 216
25 × 7 = 224
23 × 29 = 232
24 × 3 × 5 = 240
22 × 32 × 7 = 252
32 × 29 = 261
2 × 33 × 5 = 270
23 × 5 × 7 = 280
25 × 32 = 288
2 × 5 × 29 = 290
32 × 5 × 7 = 315
24 × 3 × 7 = 336
22 × 3 × 29 = 348
23 × 32 × 5 = 360
2 × 33 × 7 = 378
2 × 7 × 29 = 406
22 × 3 × 5 × 7 = 420
24 × 33 = 432
3 × 5 × 29 = 435
24 × 29 = 464
25 × 3 × 5 = 480
23 × 32 × 7 = 504
2 × 32 × 29 = 522
22 × 33 × 5 = 540
24 × 5 × 7 = 560
22 × 5 × 29 = 580
3 × 7 × 29 = 609
2 × 32 × 5 × 7 = 630
25 × 3 × 7 = 672
23 × 3 × 29 = 696
24 × 32 × 5 = 720
22 × 33 × 7 = 756
33 × 29 = 783
22 × 7 × 29 = 812
23 × 3 × 5 × 7 = 840
25 × 33 = 864
2 × 3 × 5 × 29 = 870
25 × 29 = 928
This list continues below...

... This list continues from above
33 × 5 × 7 = 945
24 × 32 × 7 = 1,008
5 × 7 × 29 = 1,015
22 × 32 × 29 = 1,044
23 × 33 × 5 = 1,080
25 × 5 × 7 = 1,120
23 × 5 × 29 = 1,160
2 × 3 × 7 × 29 = 1,218
22 × 32 × 5 × 7 = 1,260
32 × 5 × 29 = 1,305
24 × 3 × 29 = 1,392
25 × 32 × 5 = 1,440
23 × 33 × 7 = 1,512
2 × 33 × 29 = 1,566
23 × 7 × 29 = 1,624
24 × 3 × 5 × 7 = 1,680
22 × 3 × 5 × 29 = 1,740
32 × 7 × 29 = 1,827
2 × 33 × 5 × 7 = 1,890
25 × 32 × 7 = 2,016
2 × 5 × 7 × 29 = 2,030
23 × 32 × 29 = 2,088
24 × 33 × 5 = 2,160
24 × 5 × 29 = 2,320
22 × 3 × 7 × 29 = 2,436
23 × 32 × 5 × 7 = 2,520
2 × 32 × 5 × 29 = 2,610
25 × 3 × 29 = 2,784
24 × 33 × 7 = 3,024
3 × 5 × 7 × 29 = 3,045
22 × 33 × 29 = 3,132
24 × 7 × 29 = 3,248
25 × 3 × 5 × 7 = 3,360
23 × 3 × 5 × 29 = 3,480
2 × 32 × 7 × 29 = 3,654
22 × 33 × 5 × 7 = 3,780
33 × 5 × 29 = 3,915
22 × 5 × 7 × 29 = 4,060
24 × 32 × 29 = 4,176
25 × 33 × 5 = 4,320
25 × 5 × 29 = 4,640
23 × 3 × 7 × 29 = 4,872
24 × 32 × 5 × 7 = 5,040
22 × 32 × 5 × 29 = 5,220
33 × 7 × 29 = 5,481
25 × 33 × 7 = 6,048
2 × 3 × 5 × 7 × 29 = 6,090
23 × 33 × 29 = 6,264
25 × 7 × 29 = 6,496
24 × 3 × 5 × 29 = 6,960
22 × 32 × 7 × 29 = 7,308
23 × 33 × 5 × 7 = 7,560
2 × 33 × 5 × 29 = 7,830
23 × 5 × 7 × 29 = 8,120
25 × 32 × 29 = 8,352
32 × 5 × 7 × 29 = 9,135
24 × 3 × 7 × 29 = 9,744
25 × 32 × 5 × 7 = 10,080
23 × 32 × 5 × 29 = 10,440
2 × 33 × 7 × 29 = 10,962
22 × 3 × 5 × 7 × 29 = 12,180
24 × 33 × 29 = 12,528
25 × 3 × 5 × 29 = 13,920
23 × 32 × 7 × 29 = 14,616
24 × 33 × 5 × 7 = 15,120
22 × 33 × 5 × 29 = 15,660
24 × 5 × 7 × 29 = 16,240
2 × 32 × 5 × 7 × 29 = 18,270
25 × 3 × 7 × 29 = 19,488
24 × 32 × 5 × 29 = 20,880
22 × 33 × 7 × 29 = 21,924
23 × 3 × 5 × 7 × 29 = 24,360
25 × 33 × 29 = 25,056
33 × 5 × 7 × 29 = 27,405
24 × 32 × 7 × 29 = 29,232
25 × 33 × 5 × 7 = 30,240
23 × 33 × 5 × 29 = 31,320
25 × 5 × 7 × 29 = 32,480
22 × 32 × 5 × 7 × 29 = 36,540
25 × 32 × 5 × 29 = 41,760
23 × 33 × 7 × 29 = 43,848
24 × 3 × 5 × 7 × 29 = 48,720
2 × 33 × 5 × 7 × 29 = 54,810
25 × 32 × 7 × 29 = 58,464
24 × 33 × 5 × 29 = 62,640
23 × 32 × 5 × 7 × 29 = 73,080
24 × 33 × 7 × 29 = 87,696
25 × 3 × 5 × 7 × 29 = 97,440
22 × 33 × 5 × 7 × 29 = 109,620
25 × 33 × 5 × 29 = 125,280
24 × 32 × 5 × 7 × 29 = 146,160
25 × 33 × 7 × 29 = 175,392
23 × 33 × 5 × 7 × 29 = 219,240
25 × 32 × 5 × 7 × 29 = 292,320
24 × 33 × 5 × 7 × 29 = 438,480
25 × 33 × 5 × 7 × 29 = 876,960

The final answer:
(scroll down)

876,960 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 27; 28; 29; 30; 32; 35; 36; 40; 42; 45; 48; 54; 56; 58; 60; 63; 70; 72; 80; 84; 87; 90; 96; 105; 108; 112; 116; 120; 126; 135; 140; 144; 145; 160; 168; 174; 180; 189; 203; 210; 216; 224; 232; 240; 252; 261; 270; 280; 288; 290; 315; 336; 348; 360; 378; 406; 420; 432; 435; 464; 480; 504; 522; 540; 560; 580; 609; 630; 672; 696; 720; 756; 783; 812; 840; 864; 870; 928; 945; 1,008; 1,015; 1,044; 1,080; 1,120; 1,160; 1,218; 1,260; 1,305; 1,392; 1,440; 1,512; 1,566; 1,624; 1,680; 1,740; 1,827; 1,890; 2,016; 2,030; 2,088; 2,160; 2,320; 2,436; 2,520; 2,610; 2,784; 3,024; 3,045; 3,132; 3,248; 3,360; 3,480; 3,654; 3,780; 3,915; 4,060; 4,176; 4,320; 4,640; 4,872; 5,040; 5,220; 5,481; 6,048; 6,090; 6,264; 6,496; 6,960; 7,308; 7,560; 7,830; 8,120; 8,352; 9,135; 9,744; 10,080; 10,440; 10,962; 12,180; 12,528; 13,920; 14,616; 15,120; 15,660; 16,240; 18,270; 19,488; 20,880; 21,924; 24,360; 25,056; 27,405; 29,232; 30,240; 31,320; 32,480; 36,540; 41,760; 43,848; 48,720; 54,810; 58,464; 62,640; 73,080; 87,696; 97,440; 109,620; 125,280; 146,160; 175,392; 219,240; 292,320; 438,480 and 876,960
out of which 5 prime factors: 2; 3; 5; 7 and 29
876,960 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".