AP EAMCET · Maths · Permutation Combination
If \(15^k\) divides 47 ! but \(15^{k+1}\) does not divide it, then \(k=\)
- A 15
- B 12
- C 10
- D 5
Answer & Solution
Correct Answer
(C) 10
Step-by-step Solution
Detailed explanation
Since, \(15=3 \times 5\), so to find the exponent of 15 in 47 ! It is enough to find the exponent of 5 in 47 !. So, exponent of 5 in 47 !. \(=\left[\frac{47}{5}\right]+\left[\frac{47}{5^2}\right]+\ldots,\{\) where, \([x]\) is greatest integer of \(x]\). \[ =9+1 \] So, required…
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