Problem 231
The prime factorisation of binomial coefficients
The binomial coefficient 10C3 = 120.
120 = 23 × 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 10C3 is 14.
Find the sum of the terms in the prime factorisation of 20000000C15000000.
二项式系数质因数分解
二项式系数10C3 = 120。
120 = 23 × 3 × 5 = 2 × 2 × 2 × 3 × 5，而2 + 2 + 2 + 3 + 5 = 14。
因此10C3质因数分解后各项的和为14。
求20000000C15000000质因数分解后各项的和。