Let x = 224 and y = 322. If the highest common factor of 23x and a × y is divisible by x and y, then what can be the possible value of a?

A. 4

B. 12

C. 8

D. 16

Answer: Option D

Solution(By Examveda Team)

x = 224, y = 322
⇒ 23x = 23 × 224 = 23 × 16 × 14
⇒ ay = 322a = a × 23 × 14
⇒ If HCF of 23x and ay is divisible by x and y then,
23 × 16 × 14 = a × 23 × 14
a = 16