What are the divisors of 4828?

1, 2, 4, 17, 34, 68, 71, 142, 284, 1207, 2414, 4828

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, 34, 68, 142, 284, 2414, 4828

4 odd divisors

1, 17, 71, 1207

How to compute the divisors of 4828?

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 4828 by each of the numbers from 1 to 4828 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)

4828 / 1 = 4828 (the remainder is 0, so 1 is a divisor of 4828)
4828 / 2 = 2414 (the remainder is 0, so 2 is a divisor of 4828)
4828 / 3 = 1609.3333333333 (the remainder is 1, so 3 is not a divisor of 4828)
...
4828 / 4827 = 1.0002071680133 (the remainder is 1, so 4827 is not a divisor of 4828)
4828 / 4828 = 1 (the remainder is 0, so 4828 is a divisor of 4828)

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 4828 (i.e. 69.483811064161). 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 $\frac{N}{d} = D$ )

4828 / 1 = 4828 (the remainder is 0, so 1 and 4828 are divisors of 4828)
4828 / 2 = 2414 (the remainder is 0, so 2 and 2414 are divisors of 4828)
4828 / 3 = 1609.3333333333 (the remainder is 1, so 3 is not a divisor of 4828)
...
4828 / 68 = 71 (the remainder is 0, so 68 and 71 are divisors of 4828)
4828 / 69 = 69.971014492754 (the remainder is 67, so 69 is not a divisor of 4828)