Question

The prime factorisation of q has 2 and 3 only and the HCF (q,72) is 12. The no. of value(s) q can take is

a) 1 b) 2 c) 3 d) 4

Answer 1

Answer :

Prime factors of q has 2 and 3 only
And
H.C.F. ( q , 72 ) = 12
So we can say that
Prime factors of 72
72 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3
And
12 = 2 $\times$ 2 $\times$ 3
So our q will be =12

As it have prime factors
12 = 2 $\times$ 2 $\times$ 3
And
H.C.F. (12 , 72 ) = 12

So , q can have only 12 as its value . So

Option A ( Ans )