Question : 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?
Option 1: 16
Option 2: 8
Option 3: 12
Option 4: 4
Correct Answer: 16
Solution : x = 224, y = 322 HCF(Highest Common Factor) of a and b is the highest number that divides a and b exactly, leaving the remainder 0. 23 × 224 = a × 322 ⇒ a = $\frac{224}{14}$ $\therefore$ a = 16 Hence, the correct answer is 16.
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