Question

Find the number of factors of the product 5^8 * 7^5 * 2^3 which are perfect squares.

(a) 47

(b) 30

(c) 65

(d) 19

The question was asked in semester exam.

I need to ask this question from Counting topic in division Counting of Discrete Mathematics

Answer 1

The correct choice is (b) 30

For explanation I would say: Any factor of this number should be of the form 5^a * 7^b * 2^c. For the factor to be a perfect square a, b, c has to be even. a can take values 0, 2, 4, 6, 8, b can take values 0, 2, 4 and c can take values 0, 2. Total number of perfect squares = 5 * 3 * 2 = 30.