Simple math problems for recreation and research
"And yet the relation appears,
A small relation expanding like the shade
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-Wallace Stevens,'Connoisseur of Chaos' You shall find a [S] at the end of a post if solution can be found at one of its comments.Feel free to comment. HOME
Friday, August 18, 2006
Divsion problem[S]
Problem : find the maximum value of 'n' such that 18^n divides 181! See comment for clue[S]
You may be aware of the problem of type " how many zeroes does 50! end with ?". This means finding maximum 'n' such that 10^n divides 50! or 5^n divides 50! as factors of 2 are found in abundance. Now there is 5 in 5, in 10,... bit 2 fives in 25 and so on. Using the floor function [50/5]+[50/5^2]=10+2=12 50! ends with 12 zeroes.
2 comments:
You may be aware of the problem of type " how many zeroes does 50! end with ?". This means finding maximum 'n' such that 10^n divides 50! or 5^n divides 50! as factors of 2 are found in abundance. Now there is 5 in 5, in 10,... bit 2 fives in 25 and so on.
Using the floor function
[50/5]+[50/5^2]=10+2=12
50! ends with 12 zeroes.
18=3.3.2
[181/3]=60;[181/9]=20;[181/27]=6;[181/81]=2;
sum/2=44
[181/2]=90 >44
Hence, max power of 18 that divides 181! is 44.
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