Question

What fraction of the positive integer factors of 1000^3 are perfect squares? Express your answer as a common fraction.

Answer 1

1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9

Perfect square factors have even exponents.

There are 5 even exponents between 0 and 9 for each 2 and 5.

Number of perfect square factors: 5x5 =25

Total number of factors: 9x9 =81

Fraction: 25/81