How many factors of 1080 are perfect squares?



[ A ]    4
[ B ]    6
[ C ]    8
[ D ]    5 right
Answer : Option D
Explanation :
1080 = $2 3$ $\times$ $3 3$ $\times$ 5. For any perfect square, all the powers of the primes have to be even numbers. So, if the factor is of the form $2^ a$ $\times$ $3^ b$ $\times$$ 5^ c$ . 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.

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