For number N how to find x,y where x*y = N and |x - y| is minimum?

Question

I want to find numbers x and y such that x*y = N and |x-y| is minimum. For example;

7 = 7*1
15 = 5*3
16 = 4*4

Is there a fast way to find this?

In general, $x$ and $y$ will be the pair of factors closest to the square root of $N$. — angryavian, Oct 07 '20 at 23:14

score 1 · Accepted Answer · answered Oct 07 '20 at 23:22

1

Find the largest number $\le\sqrt{N}$ that divides N. Let it be $a$. Then the required solution is $x=a$, $y=N/a$.

answered Oct 07 '20 at 23:22

QED

1 Answers1