Find the maximum value of \(n\) such that \(61 \times 42 \times 26 \times 81 \times 64 \times 49 \times 47 \times 51 \times 63 \times 16 \times 67\) is perfectly divisible by \(56^n\)

Question and options

Find the maximum value of

n

such that

61 \times 42 \times 26 \times 81 \times 64 \times 49 \times 47 \times 51 \times 63 \times 16 \times 67

is perfectly divisible by

56^n

Correct answer: C - 4

56 = 2^3 x 7. Powers of 7: 42 (1), 49 (2), 63 (1) give 7^4. Powers of 2: 42 (1), 26 (1), 64 (6), 16 (4) give 2^12 = (2^3)^4. So max n = min(4,4) = 4.