## The prime factorisation of binomial coefficients

### Problem 231

Published on Friday, 6th February 2009, 01:00 pm; Solved by 3843; Difficulty rating: 40%The binomial coefficient ^{10}C_{3} = 120.

120 = 2^{3} × 3 × 5 = 2 × 2 × 2 × 3 × 5, and 2 + 2 + 2 + 3 + 5 = 14.

So the sum of the terms in the prime factorisation of ^{10}C_{3} is 14.

Find the sum of the terms in the prime factorisation of ^{20000000}C_{15000000}.