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Find the largest $n$ for which $1 2^{n}$ divides 50!.

Competition practiceNumber System, HCF & LCM

A23
B47
C16
D22

Step-by-Step Solution

12 = 2^{2} \times 3

. In 50!: power of 2 is 47 (so

2^{2}

at most 23 times), power of 3 is

16 + 5 + 1 = 22

. The limit is 22.

Answer: D) 22

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