# 328,320 and 451,440: All the common factors (divisors) and prime factors of the integer numbers

## Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd. Follow the two steps below.

### Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
continued below...
... continued from above
2 × 32 = 18
prime factor = 19
22 × 5 = 20
23 × 3 = 24
33 = 27
2 × 3 × 5 = 30
22 × 32 = 36
2 × 19 = 38
23 × 5 = 40
32 × 5 = 45
24 × 3 = 48
2 × 33 = 54
3 × 19 = 57
22 × 3 × 5 = 60
23 × 32 = 72
22 × 19 = 76
24 × 5 = 80
2 × 32 × 5 = 90
5 × 19 = 95
22 × 33 = 108
2 × 3 × 19 = 114
23 × 3 × 5 = 120
33 × 5 = 135
24 × 32 = 144
23 × 19 = 152
32 × 19 = 171
22 × 32 × 5 = 180
2 × 5 × 19 = 190
23 × 33 = 216
22 × 3 × 19 = 228
24 × 3 × 5 = 240
2 × 33 × 5 = 270
3 × 5 × 19 = 285
24 × 19 = 304
2 × 32 × 19 = 342
23 × 32 × 5 = 360
22 × 5 × 19 = 380
24 × 33 = 432
23 × 3 × 19 = 456
33 × 19 = 513
22 × 33 × 5 = 540
2 × 3 × 5 × 19 = 570
22 × 32 × 19 = 684
24 × 32 × 5 = 720
23 × 5 × 19 = 760
32 × 5 × 19 = 855
24 × 3 × 19 = 912
2 × 33 × 19 = 1,026
23 × 33 × 5 = 1,080
22 × 3 × 5 × 19 = 1,140
23 × 32 × 19 = 1,368
24 × 5 × 19 = 1,520
2 × 32 × 5 × 19 = 1,710
22 × 33 × 19 = 2,052
24 × 33 × 5 = 2,160
23 × 3 × 5 × 19 = 2,280
33 × 5 × 19 = 2,565
24 × 32 × 19 = 2,736
22 × 32 × 5 × 19 = 3,420
23 × 33 × 19 = 4,104
24 × 3 × 5 × 19 = 4,560
2 × 33 × 5 × 19 = 5,130
23 × 32 × 5 × 19 = 6,840
24 × 33 × 19 = 8,208
22 × 33 × 5 × 19 = 10,260
24 × 32 × 5 × 19 = 13,680
23 × 33 × 5 × 19 = 20,520
24 × 33 × 5 × 19 = 41,040

## Latest calculated factors (divisors)

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## Tutoring: 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 "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

• 12 = 2 × 2 × 3 = 22 × 3
• 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

#### 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 both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

• 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, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

• 1,260 = 22 × 32;
• 3,024 = 24 × 32 × 7;
• 5,544 = 23 × 32 × 7 × 11;
• Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
• GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;