how do you find the greatest common of. 16 and 42; 8 and 18; 77 and 15

Answer 1

"greatest common" what?

greatest common factor?

16 and 42:
ask yourself, what is the largest number that divides exactly into both 16 and 42.
Isn't it 2?

Method:
16 = 2*2*2*2
42=2*3*7

which numbers or group of numbers are common, I see only one 2 which is common

77 = 7*11
15 = 3*5

there are no common factors.

another exampe : 48 and 120

48 = 2*2*2*2*3
120 = 2*2*2*3*5

the highest(greatest) common factor is
2*2*2*3 or 24

check it, does 24 divide into each one?
Is there a larger number?

Answer 2

The greatest common factor is the largest number that goes evenly into both numbers.

16 is divisible by 1, 2, 4, 8, 16
42 is divisible by 1, 2, 3, 6, 7, 14, 21, 42.

The greatest common factor of 16 and 42 is 2 because it's the largest divisor of both numbers.

If you post your answers for the other two sets of numbers, we'll be glad to check them.

This site also explains GCF.

http://amby.com/educate/math/2-1_GCF.html