# CAT Practice : Number System: Factorial

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A number with exactly 3 factors - what type of number is this? Key question that you must know the answer to.

## Factorials and Factors

Q.9: Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?
1. 16
2. 12
3. 9
4. 14

Choice A. 16

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## Detailed Solution

A number with exactly 3 factors has to be square of a prime.
Now, 32 divides 25! So do 52, 72, 112.
132 will not divide 25!
So the largest number with 3 factors that divide 25! is 121.
K – 1 = 120 = 22 × 3 × 5
K – 1 has 16 factors.

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