What are the divisors of 4908?

1, 2, 3, 4, 6, 12, 409, 818, 1227, 1636, 2454, 4908

There is a total of 12 positive divisors.
The sum of these divisors is 11480.
The arithmetic mean is 956.66666666667.

8 even divisors

2, 4, 6, 12, 818, 1636, 2454, 4908

4 odd divisors

1, 3, 409, 1227

How to compute the divisors of 4908?

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 4908 by each of the numbers from 1 to 4908 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)

4908 / 1 = 4908 (the remainder is 0, so 1 is a divisor of 4908)
4908 / 2 = 2454 (the remainder is 0, so 2 is a divisor of 4908)
4908 / 3 = 1636 (the remainder is 0, so 3 is a divisor of 4908)
...
4908 / 4907 = 1.0002037905034 (the remainder is 1, so 4907 is not a divisor of 4908)
4908 / 4908 = 1 (the remainder is 0, so 4908 is a divisor of 4908)

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 4908 (i.e. 70.057119552548). 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 $\frac{N}{d} = D$ )

4908 / 1 = 4908 (the remainder is 0, so 1 and 4908 are divisors of 4908)
4908 / 2 = 2454 (the remainder is 0, so 2 and 2454 are divisors of 4908)
4908 / 3 = 1636 (the remainder is 0, so 3 and 1636 are divisors of 4908)
...
4908 / 69 = 71.130434782609 (the remainder is 9, so 69 is not a divisor of 4908)
4908 / 70 = 70.114285714286 (the remainder is 8, so 70 is not a divisor of 4908)