Finding Highest Power of Number
Concepts
Examples
Finding highest power of a number can be used to find the
- Highest power of a number that divide the factorial
- Highest power of a product of numbers that divide the factorial
- 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 successively2 | 10 |
2 | 5 |
2 | 2 |
2 | 1 |
0 |
∴ HIghest power of 2 in 10! is 8
Question 1 What will be remainder when 888^{333}+222^{888} is
divided by 5
1 | 2 |
3 | 4 |
Question 2 Find the highest power of 3 that can divide 333!
165 | 164 |
191 | 111 |
Question 3 Find the highest power of 10 that can divide 55!
50 | 25 |
13 | 12 |
Question 4 Find the highest power of 2 in 879!
879 | 871 |
850 | 820 |
Question 5 Find the highest power of 20 that can divide 200!
197 | 49 |
98 | 150 |
Question 6 Find the highest power of 5 in 125!
25 | 27 |
31 | 119 |