What are the divisors of 652?

1, 2, 4, 163, 326, 652

There is a total of 6 positive divisors.
The sum of these divisors is 1148.
The arithmetic mean is 191.33333333333.

4 even divisors

2, 4, 326, 652

2 odd divisors

1, 163

How to compute the divisors of 652?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 652 by each of the numbers from 1 to 652 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

652 / 1 = 652 (the remainder is 0, so 1 is a divisor of 652)
652 / 2 = 326 (the remainder is 0, so 2 is a divisor of 652)
652 / 3 = 217.33333333333 (the remainder is 1, so 3 is not a divisor of 652)
...
652 / 651 = 1.0015360983103 (the remainder is 1, so 651 is not a divisor of 652)
652 / 652 = 1 (the remainder is 0, so 652 is a divisor of 652)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 652 (i.e. 25.534290669607). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

652 / 1 = 652 (the remainder is 0, so 1 and 652 are divisors of 652)
652 / 2 = 326 (the remainder is 0, so 2 and 326 are divisors of 652)
652 / 3 = 217.33333333333 (the remainder is 1, so 3 is not a divisor of 652)
...
652 / 24 = 27.166666666667 (the remainder is 4, so 24 is not a divisor of 652)
652 / 25 = 26.08 (the remainder is 2, so 25 is not a divisor of 652)