CAT Practice : Number System: Factors

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We know how to find number of factors of a number. How do you find the number of factors that are perfect squares?

Number Theory - Factors

    Q.2: How many factors of 1080 are perfect squares?
    1. 4
    2. 6
    3. 8
    4. 5

 

  • Correct Answer
    Choice A. 4.

Detailed Solution

1080 = 23 * 33 * 5. For any perfect square, all the powers of the primes have to be even numbers. So, if the factor is of the form 2a * 3b * 5c.

The values 'a' can take are 0 and 2, b can take are 0 and 2, and c can take the value 0.

Totally there are 4 possibilities. 1, 4, 9, and 36.

Correct Answer: 4 Possibilities



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