Square Divisors
Number Theory
Level
3
How many divisors of 900 are perfect squares?
The answer is 8.
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let's factor 900 = 2^2 * 3^2 * 5^2. since each element is a perfect square, the number of ways to make perfect square are like the number of ways of elements in the power-set of {2^2 , 3^2, 5^2} (with multiplying the elements), which is 2^(sizeof set) = 2^3 = 8.
let's show it: {2^2} , {3^2} , {5^2} , {2^2, 3^2} , {2^2, 5^2} , {3^2, 5^2} , {2^2, 3^2, 5^2} and the empty set, which are 4, 9, 25, 36, 100, 225, 900 and 1, respectively, all are perfect squares and are divisors 0f 900.
p.s. sorry for the bad formatting im new to this.