What are the divisors of 4708?

1, 2, 4, 11, 22, 44, 107, 214, 428, 1177, 2354, 4708

There is a total of 12 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 756.

8 even divisors

2, 4, 22, 44, 214, 428, 2354, 4708

4 odd divisors

1, 11, 107, 1177

How to compute the divisors of 4708?

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 4708 by each of the numbers from 1 to 4708 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)

4708 / 1 = 4708 (the remainder is 0, so 1 is a divisor of 4708)
4708 / 2 = 2354 (the remainder is 0, so 2 is a divisor of 4708)
4708 / 3 = 1569.3333333333 (the remainder is 1, so 3 is not a divisor of 4708)
...
4708 / 4707 = 1.0002124495432 (the remainder is 1, so 4707 is not a divisor of 4708)
4708 / 4708 = 1 (the remainder is 0, so 4708 is a divisor of 4708)

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 4708 (i.e. 68.614867193634). 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 $\frac{N}{d} = D$ )

4708 / 1 = 4708 (the remainder is 0, so 1 and 4708 are divisors of 4708)
4708 / 2 = 2354 (the remainder is 0, so 2 and 2354 are divisors of 4708)
4708 / 3 = 1569.3333333333 (the remainder is 1, so 3 is not a divisor of 4708)
...
4708 / 67 = 70.268656716418 (the remainder is 18, so 67 is not a divisor of 4708)
4708 / 68 = 69.235294117647 (the remainder is 16, so 68 is not a divisor of 4708)