Q55 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

The number of proper divisors of the number obtained by dividing 13 ! with 100 is

A
216
Correct answer
B
430
C
214
D
790

Solution

$$ 13 !=2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 13 $$ 13 ! is divided by 100 Then, $\frac{13 !}{100}=2^8 \times 3^5 \times 7^1 \times 11^1 \times 13^1$ The number of proper divisor at the number obtained is $(8+1)(5+1)(1+1)(1+1)(1+1)-2$ $$ =9 \times 6 \times 2 \times 2 \times 2-2=432-2=430 $$

Hence, the correct answer is option: 'B'.

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