2018-09-30 22:01:58 +00:00
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---
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id: 5900f4531000cf542c50ff66
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title: 'Problem 231: The prime factorisation of binomial coefficients'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301875
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2021-01-13 02:31:00 +00:00
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dashedName: problem-231-the-prime-factorisation-of-binomial-coefficients
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2021-07-15 12:26:34 +00:00
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The binomial coefficient $\displaystyle\binom{10}{3} = 120$.
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2020-11-27 18:02:05 +00:00
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2021-07-15 12:26:34 +00:00
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$120 = 2^3 × 3 × 5 = 2 × 2 × 2 × 3 × 5$, and $2 + 2 + 2 + 3 + 5 = 14$.
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2020-11-27 18:02:05 +00:00
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2021-07-15 12:26:34 +00:00
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So the sum of the terms in the prime factorisation of $\displaystyle\binom{10}{3}$ is $14$.
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2018-09-30 22:01:58 +00:00
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2021-07-15 12:26:34 +00:00
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Find the sum of the terms in the prime factorisation of $\binom{20\\,000\\,000}{15\\,000\\,000}$.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2021-07-15 12:26:34 +00:00
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`primeFactorisation()` should return `7526965179680`.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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2021-07-15 12:26:34 +00:00
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assert.strictEqual(primeFactorisation(), 7526965179680);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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2021-07-15 12:26:34 +00:00
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function primeFactorisation() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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2021-07-15 12:26:34 +00:00
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primeFactorisation();
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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