The number of factors of $3^5 \times 5^8 \times 7^2$ that are perfect squares is

Question and options

The number of factors of

3^5 \times 5^8 \times 7^2

that are perfect squares is

Answer and explanation

Correct answer: B - 30

There are $30$ square factors. The exponents of $3,5,7$ must each be even, giving respectively $3,5,2$ choices when zero is included. Their product is $30$ , whereas $15$ accounts for only one choice of the exponent of $7$ .

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The number of factors of \(3^5 \times 5^8 \times 7^2\) that are perfect squares is