JEE Mains · Maths · STD 11 - 6. permutation and combination
The largest value of \( n \), for which \(40^{ n }\) divides 60!, is
- A 13
- B 11
- C 12
- D 14
Answer & Solution
Correct Answer
(D) 14
Step-by-step Solution
Detailed explanation
\(40^{ n }=2^{3 n } \times 5^{ n }\) \(E _2(60!)=\left[\frac{60}{2}\right]+\left[\frac{60}{2^2}\right]+\left[\frac{60}{2^3}\right]+\left[\frac{60}{2^4}\right]+\left[\frac{60}{2^5}\right]\) \(=30+15+7+3+1=56\) \(E _5(60!)=\left[\frac{60}{5}\right]+\left[\frac{60}{5^2}\right]\)…
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