Question

The GCF of any two even numbers is always even True. Or . False

Answer 1

Solution :-

The G.C.F. of any two even numbers will always be an even number. The statement is absolutely true. 

Explanation -

Let us take an example. 

We will find G.C.F. of 12, 24, 84 

12 = 2*2*3

84 = 2*2*3*7

Common factors of 12 and 84 = 2*2*3 

G.C.F. of 12 and 84 = 12

G.C.F. refers to the greatest common factor that two or more numbers have, and obviously it is always an even number. 

Let us take another example -

G.C.F. of 18, 30 and 42

18 = 2*3*3

30= 2*3*5

42 = 2*3*7

Common factors = 2*3

G.C.F. of 18, 30 and 42 = 6

Hence, the G.C.F. of any two even numbers is always an even number.

Answer 2

This statement is not true.

The opposite is true: the gcf of an odd number and an even number is always odd.

All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even.

Thus the only common factors between odd and even numbers must be odd.