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Number Theory Level 2

I have 2016 identical marbles. I plan to distribute them equally into one or more identical containers. How many ways can this be done if I have an unlimited number of containers?


The answer is 36.

Benedict Dimacutac by Benedict Dimacutac , 21, Philippines

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1 solution

Mike Davison
Oct 25, 2017

Since we're distributing equally, we need to calculate the number of factors.

Prime factors are 2^5, 3^2 and 7

Add 1 to each exponent and multiply them together.

(5+1)(2+1)(1+1) = 6×3×2 = 36

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I remembered this trick, but if anyone would like to expand on why it works or link to a wiki, feel free!

Mike Davison - 3 years, 7 months ago

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