Question

Is the gcf os a pair of numbers ever greater than both numbers ? explain with an example.

Answer 1

The gcf of numbers can never be greater than both numbers, because in order to be a gcf, it must be a factor that both numbers have, so if one number does not have that then it is not a gcf.

Answer 2

No, G.C.F. of pair of numbers can never be greater than both numbers.

Explanation:

G.C.F. (Greatest Common Factor) of pair of numbers is defined as the greatest factor of both the number that exactly divides both numbers.

For Example: G.C.F. of 14 and 21 =

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

Common Factors of 36 and 48 = 2 × 2 × 3 = 12

∴ G.C.F. = 12

As, we see that G.C.F. is factor of given number. So, it can never be greater than given numbers.