CAT Practice : Number System: Factors

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Given a prime factorization, how do we find how many factors of the number are perfect squares.

Number Theory - Factors

    Q.3: How many factors of 25 * 36 * 52 are perfect squares?
    1. 18
    2. 24
    3. 36
    4. 8


  • Correct Answer
    Choice B. 24.

Detailed Solution

Any factor of this number should be of the form 2a * 3b * 5c.

For the factor to be a perfect square a,b,c have to be even.

a can take values 0, 2, 4.
b can take values 0, 2, 4, 6
and c can take values 0, 2

Total number of perfect squares = 3 * 4 * 2 = 24. Choice (B).

Correct Answer: 24

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