Finding Highest Power of Number
Concepts Examples

Finding highest power of a number can be used to find the

  1. Highest power of a number that divide the factorial
  2. Highest power of a product of numbers that divide the factorial
  3. Number of 0's at the end of the factorial

To find the highest power of a number 'x' in the factorial of number N,

Step 1 : Divide the number N successively till we get 0 as the last quotient.

Step 2 : Add all the quotients to get the highest power that divides the factorial of N

e.g Find the highest power of a 2 in factorial 10.

i) To find highest power of 2 in 10! we divide 10 successively
2 10
2 5
2 2
2 1
  0
ii) Add all the quotients, i.e. 5+2+1=8

∴ HIghest power of 2 in 10! is 8

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