What is the greatest common factor of 42 63 and 84

14

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.