Question

If 14 is the HCF of 4p and 21q, then minimum value of p and q is:

• A. 1
• B. 2
• C. 2, x
• D. No common factors exist

Answer 1

The correct option is A

1

Given that,

14 is HCF of 4p and 21q.

Therefore, both of them should have 7 and 2 as prime factors.

$4p=2\times 2\times p$

$21q=3\times 7\times q$

So, $p=7,4p=4\times 7=28,$ which is a multiple of 14.

Also, $q=2,21q=21\times 2=42,$ which is a multiple of 14.

Therefore, p should be 7 and q should be 2.