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Find the highest power of 12! in 142! + 143!

Find the highest power of 12! in 142! + 143!

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2 Answers

Rohit Agarwal
20 Points
9 years ago
3
arun
13 Points
6 years ago
The highest power of 12! in 142!+143! can be found in the following way
First add 142!+142!x143
>142!(1+143)
>144x142!
 
Now we see that 144=12x12
& since we are concerned with finding the highest power of 12!(12x11x10x9......x1) We  will not consider it(pertaining to the solution)
>Now the highest power of 12! should have all the powers of 1x2x3x4x5....x12
Therefore just fing the highest power of 11 in 142!
The method will be [142/11]+[142/11x11]....& so on till 142 is divisilble by the powers of 11 .Note that [ X] is a greatest integer function so you have to take the quotient only.
 
Hence You will get the answer as 13 which is the highest power of 12! in 142!
 

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