What are the divisors of 4812?

1, 2, 3, 4, 6, 12, 401, 802, 1203, 1604, 2406, 4812

There is a total of 12 positive divisors.
The sum of these divisors is 11256.
The arithmetic mean is 938.

8 even divisors

2, 4, 6, 12, 802, 1604, 2406, 4812

4 odd divisors

1, 3, 401, 1203

How to compute the divisors of 4812?

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 4812 by each of the numbers from 1 to 4812 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)

4812 / 1 = 4812 (the remainder is 0, so 1 is a divisor of 4812)
4812 / 2 = 2406 (the remainder is 0, so 2 is a divisor of 4812)
4812 / 3 = 1604 (the remainder is 0, so 3 is a divisor of 4812)
...
4812 / 4811 = 1.0002078569944 (the remainder is 1, so 4811 is not a divisor of 4812)
4812 / 4812 = 1 (the remainder is 0, so 4812 is a divisor of 4812)

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 4812 (i.e. 69.368580784098). 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 $\frac{N}{d} = D$ )

4812 / 1 = 4812 (the remainder is 0, so 1 and 4812 are divisors of 4812)
4812 / 2 = 2406 (the remainder is 0, so 2 and 2406 are divisors of 4812)
4812 / 3 = 1604 (the remainder is 0, so 3 and 1604 are divisors of 4812)
...
4812 / 68 = 70.764705882353 (the remainder is 52, so 68 is not a divisor of 4812)
4812 / 69 = 69.739130434783 (the remainder is 51, so 69 is not a divisor of 4812)