Question

If the number of positive integral divisors of $^{13}C_6$ is m. Then m equals to

Answer 1

24

Answer 2

First, compute the value of $^{13}C_6$, which is 1716. Then, find the prime factorization of 1716 as $2^2 \times 3^1 \times 11^1 \times 13^1$. The number of positive integral divisors is found by taking each exponent, adding 1, and multiplying the results: $(2+1)(1+1)(1+1)(1+1) = 3 \times 2 \times 2 \times 2 = 24$.