Zeroes

Number Theory Level 2

Find the number of trailing zeroes in 625!

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Astro Enthusiast by Astro Enthusiast , 24, Philippines

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2 solutions

Astro Enthusiast
Jul 10, 2014

Divide the number by 5. Divide it by 25. Divide it by 125. Divide it by 625.

As long as the answer n < 5, you do not stop dividing the number by 5^x. x is the exponent.

Just get the whole numbers from the quotients and never mind the fractions.

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is it always 5?

efren pineda - 6 years, 10 months ago

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Yes. :) It is always 5.

Astro Enthusiast - 6 years, 10 months ago

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Only in trailing zeros' case, and that also because 2 2 is always much ahead of 5 5 .

Satvik Golechha - 6 years, 9 months ago

Yes, because the number is in base 10, 10 = 2 x 5, and 5 is the larger prime factor. :)

Jaydee Lucero - 6 years, 10 months ago

Hi! Could you explain the solution once again? I did not understand.

Sucheta Hande - 6 years, 10 months ago
Akhil Vinod
Aug 28, 2014

dividing 625 with 5^x upto 5^x,x<5

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