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Number Systems
January 14, 2004
How many zeros will be there in the value of 25!?
| (A) | 25 |
| (B) | 8 |
| (C) | 6 |
| (D) | 5 |
| (E) | 2 |
Correct Answer Choice (C)
Solution:
25! is factorial 25 whose value = 25*24*23*22*…..*1
When a number that has 5 as its factor is multiplied by another number that has 2 as its factor, the result will have ‘0’ in its units digit.
In 25!, the numbers that have 5 as their factor are 5, 10, 15, 20, and 25. 25 is the square of 5 and hence has two 5’s in it.
Therefore, 25! contains in it 6 fives.
There are more than 6 even numbers in 25!. Hence, the limiting factor is the number of 5s.
And hence, the number 25! will have 6 zeroes in it.
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