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Problem 231


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。

20000000C15000000质因数分解后各项的和。