What is the greatest common factor of 42 63 and 84?

Answer 1

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, 2x2 and 1x4 both equal 4, then both opposite diagonal numbers 4x3 and 2x6 equal 12, then both opposite diagonal numbers 6x4 and 3x8 equal 24 and so on.

Answer 2

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

Answer 3

21 is the answer

Answer 4

21

Answer 5

21

Answer 6

14