The exponent of 7 in the prime factorization of  100C50 is

# The exponent of 7 in the prime factorization of  is

1. A

0

2. B

2

3. C

4

4. D

none of these

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### Solution:

We have

The exponent of $7$ in $50$! is $\left[\frac{50}{7}\right]+\left[\frac{50}{{7}^{2}}\right]=7+1=8$

$\left[\frac{100}{7}\right]+\left[\frac{100}{{7}^{2}}\right]+\left[\frac{100}{{7}^{3}}\right]$$=14+2=16$

Thus, exponent of 7 in the prime factorization of  is $16-2\left(8\right)=0$

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