Question : If a number K = 42 × 25 × 54 × 135 is divisible by 3a, then find the maximum value of a.
Option 1: 6
Option 2: 7
Option 3: 4
Option 4: 5
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Correct Answer: 7
Solution : Given number, K = 42 × 25 × 54 × 135 = 3 × 14 × 25 × 3 3 × 2 × 3 3 × 5 ⇒ K = 3 7 × 14 × 25 × 2 × 5 So, the maximum power of 3 is 7. So, the value of a must be 7. Hence, the correct answer is 7.
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