# Given the Number 769,080, Calculate (Find) All the Factors (All the Divisors) of the Number 769,080 (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
22 × 3 = 12
prime factor = 13
3 × 5 = 15
prime factor = 17
22 × 5 = 20
23 × 3 = 24
2 × 13 = 26
prime factor = 29
2 × 3 × 5 = 30
2 × 17 = 34
3 × 13 = 39
23 × 5 = 40
3 × 17 = 51
22 × 13 = 52
2 × 29 = 58
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
2 × 3 × 13 = 78
5 × 17 = 85
3 × 29 = 87
2 × 3 × 17 = 102
23 × 13 = 104
22 × 29 = 116
23 × 3 × 5 = 120
2 × 5 × 13 = 130
23 × 17 = 136
5 × 29 = 145
22 × 3 × 13 = 156
2 × 5 × 17 = 170
2 × 3 × 29 = 174
3 × 5 × 13 = 195
22 × 3 × 17 = 204
13 × 17 = 221
23 × 29 = 232
3 × 5 × 17 = 255
22 × 5 × 13 = 260
2 × 5 × 29 = 290
23 × 3 × 13 = 312
22 × 5 × 17 = 340
22 × 3 × 29 = 348
13 × 29 = 377
2 × 3 × 5 × 13 = 390
23 × 3 × 17 = 408
3 × 5 × 29 = 435
2 × 13 × 17 = 442
17 × 29 = 493
2 × 3 × 5 × 17 = 510
23 × 5 × 13 = 520
22 × 5 × 29 = 580
3 × 13 × 17 = 663
23 × 5 × 17 = 680
23 × 3 × 29 = 696
2 × 13 × 29 = 754
22 × 3 × 5 × 13 = 780
2 × 3 × 5 × 29 = 870
This list continues below...

... This list continues from above
22 × 13 × 17 = 884
2 × 17 × 29 = 986
22 × 3 × 5 × 17 = 1,020
5 × 13 × 17 = 1,105
3 × 13 × 29 = 1,131
23 × 5 × 29 = 1,160
2 × 3 × 13 × 17 = 1,326
3 × 17 × 29 = 1,479
22 × 13 × 29 = 1,508
23 × 3 × 5 × 13 = 1,560
22 × 3 × 5 × 29 = 1,740
23 × 13 × 17 = 1,768
5 × 13 × 29 = 1,885
22 × 17 × 29 = 1,972
23 × 3 × 5 × 17 = 2,040
2 × 5 × 13 × 17 = 2,210
2 × 3 × 13 × 29 = 2,262
5 × 17 × 29 = 2,465
22 × 3 × 13 × 17 = 2,652
2 × 3 × 17 × 29 = 2,958
23 × 13 × 29 = 3,016
3 × 5 × 13 × 17 = 3,315
23 × 3 × 5 × 29 = 3,480
2 × 5 × 13 × 29 = 3,770
23 × 17 × 29 = 3,944
22 × 5 × 13 × 17 = 4,420
22 × 3 × 13 × 29 = 4,524
2 × 5 × 17 × 29 = 4,930
23 × 3 × 13 × 17 = 5,304
3 × 5 × 13 × 29 = 5,655
22 × 3 × 17 × 29 = 5,916
13 × 17 × 29 = 6,409
2 × 3 × 5 × 13 × 17 = 6,630
3 × 5 × 17 × 29 = 7,395
22 × 5 × 13 × 29 = 7,540
23 × 5 × 13 × 17 = 8,840
23 × 3 × 13 × 29 = 9,048
22 × 5 × 17 × 29 = 9,860
2 × 3 × 5 × 13 × 29 = 11,310
23 × 3 × 17 × 29 = 11,832
2 × 13 × 17 × 29 = 12,818
22 × 3 × 5 × 13 × 17 = 13,260
2 × 3 × 5 × 17 × 29 = 14,790
23 × 5 × 13 × 29 = 15,080
3 × 13 × 17 × 29 = 19,227
23 × 5 × 17 × 29 = 19,720
22 × 3 × 5 × 13 × 29 = 22,620
22 × 13 × 17 × 29 = 25,636
23 × 3 × 5 × 13 × 17 = 26,520
22 × 3 × 5 × 17 × 29 = 29,580
5 × 13 × 17 × 29 = 32,045
2 × 3 × 13 × 17 × 29 = 38,454
23 × 3 × 5 × 13 × 29 = 45,240
23 × 13 × 17 × 29 = 51,272
23 × 3 × 5 × 17 × 29 = 59,160
2 × 5 × 13 × 17 × 29 = 64,090
22 × 3 × 13 × 17 × 29 = 76,908
3 × 5 × 13 × 17 × 29 = 96,135
22 × 5 × 13 × 17 × 29 = 128,180
23 × 3 × 13 × 17 × 29 = 153,816
2 × 3 × 5 × 13 × 17 × 29 = 192,270
23 × 5 × 13 × 17 × 29 = 256,360
22 × 3 × 5 × 13 × 17 × 29 = 384,540
23 × 3 × 5 × 13 × 17 × 29 = 769,080

## The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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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".