What are the divisors of 4636?

1, 2, 4, 19, 38, 61, 76, 122, 244, 1159, 2318, 4636

There is a total of 12 positive divisors.
The sum of these divisors is 8680.
The arithmetic mean is 723.33333333333.

8 even divisors

2, 4, 38, 76, 122, 244, 2318, 4636

4 odd divisors

1, 19, 61, 1159

How to compute the divisors of 4636?

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 4636 by each of the numbers from 1 to 4636 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)

4636 / 1 = 4636 (the remainder is 0, so 1 is a divisor of 4636)
4636 / 2 = 2318 (the remainder is 0, so 2 is a divisor of 4636)
4636 / 3 = 1545.3333333333 (the remainder is 1, so 3 is not a divisor of 4636)
...
4636 / 4635 = 1.0002157497303 (the remainder is 1, so 4635 is not a divisor of 4636)
4636 / 4636 = 1 (the remainder is 0, so 4636 is a divisor of 4636)

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 4636 (i.e. 68.088178122197). 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 $\frac{N}{d} = D$ )

4636 / 1 = 4636 (the remainder is 0, so 1 and 4636 are divisors of 4636)
4636 / 2 = 2318 (the remainder is 0, so 2 and 2318 are divisors of 4636)
4636 / 3 = 1545.3333333333 (the remainder is 1, so 3 is not a divisor of 4636)
...
4636 / 67 = 69.194029850746 (the remainder is 13, so 67 is not a divisor of 4636)
4636 / 68 = 68.176470588235 (the remainder is 12, so 68 is not a divisor of 4636)