CAT Practice : Number System: Factors

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How many factors does a number have? Thats a straightforward qn. How many factors of a number are odd; now thats an interesting variant.

Number Theory - Odd Factors

    Q.4: How many factors of 24 * 53 * 74 are odd numbers?
    1. 100
    2. 99
    3. 20
    4. 24

 

  • Correct Answer
    Choice C. 20.

Detailed Solution

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

For the factor to be an odd number,
a should be 0.
b can take values 0, 1, 2, 3.
and c can take values 0, 1, 2, 3, 4.

Total number of odd factors = 4 * 5 = 20.
Choice (C)

Correct Answer: 20



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