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Question

# How many even factors does the number 720 have in all?

A

10

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B

30

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C

20

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D

24

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Solution

## The correct option is D 24 An even number 2m is a factor of 720 if and only if m is a factor of 360. So it is the same as counting the divisors/ factors of 360. Now, 360 can be written as follows as the product of its primes: 360=2×2×2×3×3×5 Thus, 360 has (3+1) ×(2+1) ×(1+1) factors in all. i.e., 720 has (3+1) ×(2+1) ×(1+1) even factors in all. ⟹ 720 has 4 × 3× 2= 24 even factors in all.

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