Given the Number 884,520, Calculate (Find) All the Factors (All the Divisors) of the Number 884,520 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 884,520

1. Carry out the prime factorization of the number 884,520:

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


884,520 = 23 × 35 × 5 × 7 × 13
884,520 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 884,520

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
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
5 × 7 = 35
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
22 × 13 = 52
2 × 33 = 54
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 5 × 7 = 70
23 × 32 = 72
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
23 × 13 = 104
3 × 5 × 7 = 105
22 × 33 = 108
32 × 13 = 117
23 × 3 × 5 = 120
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
22 × 3 × 13 = 156
2 × 34 = 162
23 × 3 × 7 = 168
22 × 32 × 5 = 180
2 × 7 × 13 = 182
33 × 7 = 189
3 × 5 × 13 = 195
2 × 3 × 5 × 7 = 210
23 × 33 = 216
2 × 32 × 13 = 234
35 = 243
22 × 32 × 7 = 252
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
23 × 5 × 7 = 280
23 × 3 × 13 = 312
32 × 5 × 7 = 315
22 × 34 = 324
33 × 13 = 351
23 × 32 × 5 = 360
22 × 7 × 13 = 364
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
34 × 5 = 405
22 × 3 × 5 × 7 = 420
5 × 7 × 13 = 455
22 × 32 × 13 = 468
2 × 35 = 486
23 × 32 × 7 = 504
23 × 5 × 13 = 520
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
34 × 7 = 567
32 × 5 × 13 = 585
2 × 32 × 5 × 7 = 630
23 × 34 = 648
2 × 33 × 13 = 702
23 × 7 × 13 = 728
22 × 33 × 7 = 756
22 × 3 × 5 × 13 = 780
2 × 34 × 5 = 810
32 × 7 × 13 = 819
23 × 3 × 5 × 7 = 840
2 × 5 × 7 × 13 = 910
23 × 32 × 13 = 936
This list continues below...

... This list continues from above
33 × 5 × 7 = 945
22 × 35 = 972
34 × 13 = 1,053
23 × 33 × 5 = 1,080
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
2 × 32 × 5 × 13 = 1,170
35 × 5 = 1,215
22 × 32 × 5 × 7 = 1,260
3 × 5 × 7 × 13 = 1,365
22 × 33 × 13 = 1,404
23 × 33 × 7 = 1,512
23 × 3 × 5 × 13 = 1,560
22 × 34 × 5 = 1,620
2 × 32 × 7 × 13 = 1,638
35 × 7 = 1,701
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 33 × 5 × 7 = 1,890
23 × 35 = 1,944
2 × 34 × 13 = 2,106
23 × 3 × 7 × 13 = 2,184
22 × 34 × 7 = 2,268
22 × 32 × 5 × 13 = 2,340
2 × 35 × 5 = 2,430
33 × 7 × 13 = 2,457
23 × 32 × 5 × 7 = 2,520
2 × 3 × 5 × 7 × 13 = 2,730
23 × 33 × 13 = 2,808
34 × 5 × 7 = 2,835
35 × 13 = 3,159
23 × 34 × 5 = 3,240
22 × 32 × 7 × 13 = 3,276
2 × 35 × 7 = 3,402
2 × 33 × 5 × 13 = 3,510
23 × 5 × 7 × 13 = 3,640
22 × 33 × 5 × 7 = 3,780
32 × 5 × 7 × 13 = 4,095
22 × 34 × 13 = 4,212
23 × 34 × 7 = 4,536
23 × 32 × 5 × 13 = 4,680
22 × 35 × 5 = 4,860
2 × 33 × 7 × 13 = 4,914
34 × 5 × 13 = 5,265
22 × 3 × 5 × 7 × 13 = 5,460
2 × 34 × 5 × 7 = 5,670
2 × 35 × 13 = 6,318
23 × 32 × 7 × 13 = 6,552
22 × 35 × 7 = 6,804
22 × 33 × 5 × 13 = 7,020
34 × 7 × 13 = 7,371
23 × 33 × 5 × 7 = 7,560
2 × 32 × 5 × 7 × 13 = 8,190
23 × 34 × 13 = 8,424
35 × 5 × 7 = 8,505
23 × 35 × 5 = 9,720
22 × 33 × 7 × 13 = 9,828
2 × 34 × 5 × 13 = 10,530
23 × 3 × 5 × 7 × 13 = 10,920
22 × 34 × 5 × 7 = 11,340
33 × 5 × 7 × 13 = 12,285
22 × 35 × 13 = 12,636
23 × 35 × 7 = 13,608
23 × 33 × 5 × 13 = 14,040
2 × 34 × 7 × 13 = 14,742
35 × 5 × 13 = 15,795
22 × 32 × 5 × 7 × 13 = 16,380
2 × 35 × 5 × 7 = 17,010
23 × 33 × 7 × 13 = 19,656
22 × 34 × 5 × 13 = 21,060
35 × 7 × 13 = 22,113
23 × 34 × 5 × 7 = 22,680
2 × 33 × 5 × 7 × 13 = 24,570
23 × 35 × 13 = 25,272
22 × 34 × 7 × 13 = 29,484
2 × 35 × 5 × 13 = 31,590
23 × 32 × 5 × 7 × 13 = 32,760
22 × 35 × 5 × 7 = 34,020
34 × 5 × 7 × 13 = 36,855
23 × 34 × 5 × 13 = 42,120
2 × 35 × 7 × 13 = 44,226
22 × 33 × 5 × 7 × 13 = 49,140
23 × 34 × 7 × 13 = 58,968
22 × 35 × 5 × 13 = 63,180
23 × 35 × 5 × 7 = 68,040
2 × 34 × 5 × 7 × 13 = 73,710
22 × 35 × 7 × 13 = 88,452
23 × 33 × 5 × 7 × 13 = 98,280
35 × 5 × 7 × 13 = 110,565
23 × 35 × 5 × 13 = 126,360
22 × 34 × 5 × 7 × 13 = 147,420
23 × 35 × 7 × 13 = 176,904
2 × 35 × 5 × 7 × 13 = 221,130
23 × 34 × 5 × 7 × 13 = 294,840
22 × 35 × 5 × 7 × 13 = 442,260
23 × 35 × 5 × 7 × 13 = 884,520

The final answer:
(scroll down)

884,520 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 13; 14; 15; 18; 20; 21; 24; 26; 27; 28; 30; 35; 36; 39; 40; 42; 45; 52; 54; 56; 60; 63; 65; 70; 72; 78; 81; 84; 90; 91; 104; 105; 108; 117; 120; 126; 130; 135; 140; 156; 162; 168; 180; 182; 189; 195; 210; 216; 234; 243; 252; 260; 270; 273; 280; 312; 315; 324; 351; 360; 364; 378; 390; 405; 420; 455; 468; 486; 504; 520; 540; 546; 567; 585; 630; 648; 702; 728; 756; 780; 810; 819; 840; 910; 936; 945; 972; 1,053; 1,080; 1,092; 1,134; 1,170; 1,215; 1,260; 1,365; 1,404; 1,512; 1,560; 1,620; 1,638; 1,701; 1,755; 1,820; 1,890; 1,944; 2,106; 2,184; 2,268; 2,340; 2,430; 2,457; 2,520; 2,730; 2,808; 2,835; 3,159; 3,240; 3,276; 3,402; 3,510; 3,640; 3,780; 4,095; 4,212; 4,536; 4,680; 4,860; 4,914; 5,265; 5,460; 5,670; 6,318; 6,552; 6,804; 7,020; 7,371; 7,560; 8,190; 8,424; 8,505; 9,720; 9,828; 10,530; 10,920; 11,340; 12,285; 12,636; 13,608; 14,040; 14,742; 15,795; 16,380; 17,010; 19,656; 21,060; 22,113; 22,680; 24,570; 25,272; 29,484; 31,590; 32,760; 34,020; 36,855; 42,120; 44,226; 49,140; 58,968; 63,180; 68,040; 73,710; 88,452; 98,280; 110,565; 126,360; 147,420; 176,904; 221,130; 294,840; 442,260 and 884,520
out of which 5 prime factors: 2; 3; 5; 7 and 13
884,520 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

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".