Question
The largest value of n, for which 40^ n divides 60!, is
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 11
- B. 12
- C. 14
- D. 13
Answer
C. 14
Step-by-step solution
40^n = 2^ 3n 5^n. We need the highest power of 40 dividing 60!. Power of 5 in 60! = 60/5 + 60/25 = 12 + 2 = 14. Power of 2 in 60! = 60/2 + 60/4 + 60/8 + 60/16 + 60/32 = 30 + 15 + 7 + 3 + 1 = 56. We need n 14 and 3n 56 (i.e., n 18). The binding constraint is n 14, so the largest value is n = 14.
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