cat question from number theory factorials.

1. Number Theory

2. Number Theory
Let K be the largest number with exactly 3 factors that divide 25!
How many factors does (k – 1) have?
(a) 16 (b) 12
(c) 9 (d) 14

3. Number Theory
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 = 23 × 3 × 5
K – 1 has 16 factors.
Answer choice (a)
Let K be the largest number with exactly 3 factors that divide 25!
How many factors does (k – 1) have?

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