Question

For which pairs of numbers is 6 a common factor?

Choose all answers that are correct.
A.) 12 and 20
B.) 18 and 24
C.) 30 and 54
D.) 42 and 56

Answer 1

Commen factor means you can get integers after division.

A. 20 is not correct

B. Correct

C. Correct

D. 56 is not correct

Answer 2

easy way is to list multipules of 6
6,12,18,24,30,36,42,48,54
so we can see that A doesn't work because 20 doesn't have 6 as a common factor
C works
D doesn't work because of the 56


answers are B and C



another way is to factor each
notice that 6=2*3
so factor each and see if we can find a 2*3 in each

A.
12=2*2*3, so there is a 6
20=2*2*5, not 6

B.
18=2*3*3, so there is a 6
24=2*2*3*3, so there is a 6
works

C.
30=2*3*5, there is a 6
54=2*3*3*3, there is a 6
works

D.
42=2*3*7, there is a 6
56=2*2*2*7, there isn't a 6
nope

answes are B and C