What is the greatest common factor of 42 63 and 84

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21 is the answer

14

21

21

The greatest common factor for 63, 42, and 84 is 21.

The Greatest Common Factor (GCF) of 84, 63, and 42 is 21.

The greatest common factor is either the difference between the

numbers or a factor of the difference between the numbers.

Note: 84 – 63 = 21 and 63 – 42 = 21. So, the greatest common

factor might be 21.

When you divide each of the numbers by 21, it divides evenly, so

21 is the greatest common factor.

Another way to determine the greatest common factor is to find

all the factors of the numbers and compare them.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The factors of 63 are 1, 3, 7, 9, 21, and 63.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and

84.

The common factors are 1, 3, 7, and 21.

Therefore, the greatest common factor is 21.

The greatest common factor can also be calculated by identifying

the common prime factors and multiplying them together.

The prime factors of 42 are 2, 3, and 7.

The prime factors of 63 are 3, 3, and 7.

The prime factors of 84 are 2, 2, 3, and 7.

The prime factors in common are 3 and 7, so the greatest common

factor is 3 x 7 = 21.

21 is the only positive integer that exhibits the Perfect

Progression where if the multiples of 21 up to 210 are placed in to

two parallel vertical columns so that the first reads 2, 4, 6, 8,

10 etc and the second 1, 2, 3, 4, 5 etc for example,

2 4

4 2

6 3

8 4

10 5

whereby each in one column multiplied by another number ordered

diagonally in the other column equals the multiplication of the

opposite diagonal, for example, 2×2 and 1×4 both equal 4, then both

opposite diagonal numbers 4×3 and 2×6 equal 12, then both opposite

diagonal numbers 6×4 and 3×8 equal 24 and so on.