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There is one question: Prove that 33 ! is divisible by 2^15. What is the largest integer n such that 33! is divisible by 2n?

Vageesh Hegde

CA Foundation

★ 0

14-Jul-24 07:28

196

Answers (2)

Is that n is 31?

Bala Chandar

CA Inter

★ 5K+

14-Jul-24 08:14

In terms of prime factors 33! can be written as 2^a ⋅ 3^b 5^c ⋅ 7^d … (33!)=33/2+33/2^2+33/2^3+33/2^4+33/2^5 =16+8+4+2+1=31 Hence, the exponent of 2 in 33! is 31. ∴ Largest value of n is 31.

Pavan Kumar

Faculty

16-Jul-24 21:53

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