Question

The exponent of 11 in the prime factorization of 300! is

• A. 27
• B. 28
• C. 29
• D. 30

Answer 1

The correct option is C 29

In 300!, distinct numbers divisible by
11 = |$\frac{300}{11}$| = 27
Since these 27 numbers conytains, same number which can be further divisible by 11 i.e.
|$\frac{27}{11}$| = 2(121 and 242)
So, total number of 11's = 27 +2 = 29
Hence exponent of 11 is 29