Question

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

• A. 10
• B. 30
• C. 20
• D. 24

Answer 1

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:

$360=2\times 2\times 2\times 3\times 3\times 5$

Thus, 360 has $(3+1)\times (2+1)\times (1+1)$ factors in all.

i.e., 720 has $(3+1)\times (2+1)\times (1+1)$ even factors in all.
$⟹$ 720 has $4\times 3\times 2=24$ even factors in all.