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Easy

Question

# The maximum value of P such that 3^{P} divides 99 × 97 × 95 × .... × 51 is-

- 11
- 14
- 13
- 12

## The correct answer is: 14

### 99 × 97 × 95 ×....× 51

maximum power of 3 in 100 !

= 33 + 11 + 3 + 1 = 48.

maximum power of 3 in 50! =

= 16 + 5 + 1 = 22

maximum power of 3 in 25! =

= 8 + 2 = 10

exponent of 3 = 48 + 10 –

(22 × 2) = 14

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