# Given the Number 892,320, Calculate (Find) All the Factors (All the Divisors) of the Number 892,320 (the Proper, the Improper and the Prime Factors)

## 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
23 = 8
2 × 5 = 10
prime factor = 11
22 × 3 = 12
prime factor = 13
3 × 5 = 15
24 = 16
22 × 5 = 20
2 × 11 = 22
23 × 3 = 24
2 × 13 = 26
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
3 × 13 = 39
23 × 5 = 40
22 × 11 = 44
24 × 3 = 48
22 × 13 = 52
5 × 11 = 55
22 × 3 × 5 = 60
5 × 13 = 65
2 × 3 × 11 = 66
2 × 3 × 13 = 78
24 × 5 = 80
23 × 11 = 88
25 × 3 = 96
23 × 13 = 104
2 × 5 × 11 = 110
23 × 3 × 5 = 120
2 × 5 × 13 = 130
22 × 3 × 11 = 132
11 × 13 = 143
22 × 3 × 13 = 156
25 × 5 = 160
3 × 5 × 11 = 165
132 = 169
24 × 11 = 176
3 × 5 × 13 = 195
24 × 13 = 208
22 × 5 × 11 = 220
24 × 3 × 5 = 240
22 × 5 × 13 = 260
23 × 3 × 11 = 264
2 × 11 × 13 = 286
23 × 3 × 13 = 312
2 × 3 × 5 × 11 = 330
2 × 132 = 338
25 × 11 = 352
2 × 3 × 5 × 13 = 390
25 × 13 = 416
3 × 11 × 13 = 429
23 × 5 × 11 = 440
25 × 3 × 5 = 480
3 × 132 = 507
23 × 5 × 13 = 520
24 × 3 × 11 = 528
22 × 11 × 13 = 572
24 × 3 × 13 = 624
22 × 3 × 5 × 11 = 660
22 × 132 = 676
5 × 11 × 13 = 715
22 × 3 × 5 × 13 = 780
5 × 132 = 845
2 × 3 × 11 × 13 = 858
24 × 5 × 11 = 880
This list continues below...

... This list continues from above
2 × 3 × 132 = 1,014
24 × 5 × 13 = 1,040
25 × 3 × 11 = 1,056
23 × 11 × 13 = 1,144
25 × 3 × 13 = 1,248
23 × 3 × 5 × 11 = 1,320
23 × 132 = 1,352
2 × 5 × 11 × 13 = 1,430
23 × 3 × 5 × 13 = 1,560
2 × 5 × 132 = 1,690
22 × 3 × 11 × 13 = 1,716
25 × 5 × 11 = 1,760
11 × 132 = 1,859
22 × 3 × 132 = 2,028
25 × 5 × 13 = 2,080
3 × 5 × 11 × 13 = 2,145
24 × 11 × 13 = 2,288
3 × 5 × 132 = 2,535
24 × 3 × 5 × 11 = 2,640
24 × 132 = 2,704
22 × 5 × 11 × 13 = 2,860
24 × 3 × 5 × 13 = 3,120
22 × 5 × 132 = 3,380
23 × 3 × 11 × 13 = 3,432
2 × 11 × 132 = 3,718
23 × 3 × 132 = 4,056
2 × 3 × 5 × 11 × 13 = 4,290
25 × 11 × 13 = 4,576
2 × 3 × 5 × 132 = 5,070
25 × 3 × 5 × 11 = 5,280
25 × 132 = 5,408
3 × 11 × 132 = 5,577
23 × 5 × 11 × 13 = 5,720
25 × 3 × 5 × 13 = 6,240
23 × 5 × 132 = 6,760
24 × 3 × 11 × 13 = 6,864
22 × 11 × 132 = 7,436
24 × 3 × 132 = 8,112
22 × 3 × 5 × 11 × 13 = 8,580
5 × 11 × 132 = 9,295
22 × 3 × 5 × 132 = 10,140
2 × 3 × 11 × 132 = 11,154
24 × 5 × 11 × 13 = 11,440
24 × 5 × 132 = 13,520
25 × 3 × 11 × 13 = 13,728
23 × 11 × 132 = 14,872
25 × 3 × 132 = 16,224
23 × 3 × 5 × 11 × 13 = 17,160
2 × 5 × 11 × 132 = 18,590
23 × 3 × 5 × 132 = 20,280
22 × 3 × 11 × 132 = 22,308
25 × 5 × 11 × 13 = 22,880
25 × 5 × 132 = 27,040
3 × 5 × 11 × 132 = 27,885
24 × 11 × 132 = 29,744
24 × 3 × 5 × 11 × 13 = 34,320
22 × 5 × 11 × 132 = 37,180
24 × 3 × 5 × 132 = 40,560
23 × 3 × 11 × 132 = 44,616
2 × 3 × 5 × 11 × 132 = 55,770
25 × 11 × 132 = 59,488
25 × 3 × 5 × 11 × 13 = 68,640
23 × 5 × 11 × 132 = 74,360
25 × 3 × 5 × 132 = 81,120
24 × 3 × 11 × 132 = 89,232
22 × 3 × 5 × 11 × 132 = 111,540
24 × 5 × 11 × 132 = 148,720
25 × 3 × 11 × 132 = 178,464
23 × 3 × 5 × 11 × 132 = 223,080
25 × 5 × 11 × 132 = 297,440
24 × 3 × 5 × 11 × 132 = 446,160
25 × 3 × 5 × 11 × 132 = 892,320

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## 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".