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Q.

In the prime factorization of $37! = 2^{α_{2}} . 3^{α_{3}} . 5^{α_{5}} . . . . . . . . . . . 37^{α_{37}}$ the ratio $α_{3} : α_{5} =$

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a

8:21

b

17:8

c

3:5

d

5:3

answer is B.

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Detailed Solution

$37! = 2^{α_{2}} 3^{α_{3}} 5^{α_{5}} \dots \dots 37^{α_{37}}$

$α_{3} = [\frac{37}{3}] + [\frac{37}{3^{2}}] + [\frac{37}{3^{3}}] = 12 + 4 + 1 = 17$

$α_{5} = [\frac{37}{5}] + [\frac{37}{5^{2}}] = 7 + 1 = 8$

$α_{3} : α_{5} = 17 : 8$

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