AP EAMCET · Maths · Permutation Combination
In the prime factorization of \(37 !=2^{\alpha_2} \cdot 3^{\alpha_3} \cdot 5^{\alpha_5} \ldots 37^{\alpha_{37}}\) the ratio \(\alpha_3: \alpha_5=\)
- A \(3: 5\)
- B \(17: 8\)
- C \(5: 3\)
- D \(8: 21\)
Answer & Solution
Correct Answer
(B) \(17: 8\)
Step-by-step Solution
Detailed explanation
\(\alpha_3 = \lfloor \frac{37}{3} \rfloor + \lfloor \frac{37}{9} \rfloor + \lfloor \frac{37}{27} \rfloor = 12 + 4 + 1 = 17\) \(\alpha_5 = \lfloor \frac{37}{5} \rfloor + \lfloor \frac{37}{25} \rfloor = 7 + 1 = 8\) \(\alpha_3 : \alpha_5 = 17 : 8\)
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