If y is the smallest positive integer such that 3,150 multiplied by y is the square on an integer, then y must be
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
[spoiler]
3,150 = 2 x 3^2 x 5^2 x 7
so, (2)(7) = 14
Okay, I get the first step where you have to solve this question by breaking the number down to its prime factors. I just need to understand why we multiply 2 x 7. Is this because 2 and 7 are not even powers like 3 and 5 (in context of a perfect square)?
OG Explanation: To be a perfect square, 3,150 y must have an even number of prime factors (Agreed). At a minimum, y must have one factor of 2 and one factor of 7 so that 3,150y has two factors of each of the primes 2, 3, 5, and 7. The smallest integer value of y is then (2)(7) = 14.
[/spoiler]
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
[spoiler]
3,150 = 2 x 3^2 x 5^2 x 7
so, (2)(7) = 14
Okay, I get the first step where you have to solve this question by breaking the number down to its prime factors. I just need to understand why we multiply 2 x 7. Is this because 2 and 7 are not even powers like 3 and 5 (in context of a perfect square)?
OG Explanation: To be a perfect square, 3,150 y must have an even number of prime factors (Agreed). At a minimum, y must have one factor of 2 and one factor of 7 so that 3,150y has two factors of each of the primes 2, 3, 5, and 7. The smallest integer value of y is then (2)(7) = 14.
[/spoiler]
