What are the divisors of 4856?

1, 2, 4, 8, 607, 1214, 2428, 4856

There is a total of 8 positive divisors.
The sum of these divisors is 9120.
The arithmetic mean is 1140.

6 even divisors

2, 4, 8, 1214, 2428, 4856

2 odd divisors

1, 607

How to compute the divisors of 4856?

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 4856 by each of the numbers from 1 to 4856 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)

4856 / 1 = 4856 (the remainder is 0, so 1 is a divisor of 4856)
4856 / 2 = 2428 (the remainder is 0, so 2 is a divisor of 4856)
4856 / 3 = 1618.6666666667 (the remainder is 2, so 3 is not a divisor of 4856)
...
4856 / 4855 = 1.0002059732235 (the remainder is 1, so 4855 is not a divisor of 4856)
4856 / 4856 = 1 (the remainder is 0, so 4856 is a divisor of 4856)

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 4856 (i.e. 69.685005560737). 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 $\frac{N}{d} = D$ )

4856 / 1 = 4856 (the remainder is 0, so 1 and 4856 are divisors of 4856)
4856 / 2 = 2428 (the remainder is 0, so 2 and 2428 are divisors of 4856)
4856 / 3 = 1618.6666666667 (the remainder is 2, so 3 is not a divisor of 4856)
...
4856 / 68 = 71.411764705882 (the remainder is 28, so 68 is not a divisor of 4856)
4856 / 69 = 70.376811594203 (the remainder is 26, so 69 is not a divisor of 4856)