Number theory

Number Theory Level 2

Find the number of trailing zeros when 50! is expanded.

9 8 13 12 11 10

Lov Kumar by Lov Kumar , 27, India

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3 solutions

Bhavesh Yadav
Oct 1, 2015

(50/5)+(50/25)=12

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain this in more detail? For example, where did the 5 and 25 come from?

Andy Wong - 5 years, 8 months ago

correct Thanks!

Lov Kumar - 5 years, 8 months ago
Áron Bán-Szabó
Jul 10, 2017

∑ k = 1 ∞ ⌊ 50 5 k ⌋ = 12 \sum_{k=1}^{\infty} \left\lfloor\dfrac{50}{5^k}\right\rfloor=12

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Zero appears when a 5 is multiplied by an even number so the number of fives will be the number of zeros

Factorizing 50 .. Will give us 10×5 which is 10 fives and 2×25 which is 2 fives

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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