Mental maths

Number Theory Level 3

Find the number of trailing 0 0 s in 4617 ! 4617! .


The answer is 1151.

Kritarth Lohomi by kritarth lohomi , 18, India

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2 solutions

Parth Lohomi
Sep 16, 2014

[ 4617 5 \frac{4617}{5} ] +[ 4617 25 \frac{4617}{25} ] +[ 4617 125 \frac{4617}{125} ] +[ 4617 625 \frac{4617}{625} ] +[ 4617 3125 \frac{4617}{3125} ] =1151

Where [•]is the GIF

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Ramiel To-ong
Jun 19, 2015

51 : 4617 ÷ 5 = 923.4, so I get 923 factors of 5 52 : 4617 ÷ 25 = 184.68, so I get 184 additional factors of 5 53 : 4617 ÷ 125 = 36.936, so I get 36 additional factors of 5 54 : 4617 ÷ 625 = 7.3872, so I get 7 additional factors of 5 55 : 4617 ÷ 3125 = 1.47744, so I get 1 more factor of 5 56 : 4617 ÷ 15625 = 0.295488, which is less than 1, so I stop here. 

Then 4617! has 923 + 184 + 36 + 7 + 1 = 1151 trailing zeroes.
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