What are the divisors of 4857?

1, 3, 1619, 4857

There is a total of 4 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 1620.

4 odd divisors

1, 3, 1619, 4857

How to compute the divisors of 4857?

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 4857 by each of the numbers from 1 to 4857 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)

4857 / 1 = 4857 (the remainder is 0, so 1 is a divisor of 4857)
4857 / 2 = 2428.5 (the remainder is 1, so 2 is not a divisor of 4857)
4857 / 3 = 1619 (the remainder is 0, so 3 is a divisor of 4857)
...
4857 / 4856 = 1.0002059308072 (the remainder is 1, so 4856 is not a divisor of 4857)
4857 / 4857 = 1 (the remainder is 0, so 4857 is a divisor of 4857)

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 4857 (i.e. 69.692180336104). 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 $\frac{N}{d} = D$ )

4857 / 1 = 4857 (the remainder is 0, so 1 and 4857 are divisors of 4857)
4857 / 2 = 2428.5 (the remainder is 1, so 2 is not a divisor of 4857)
4857 / 3 = 1619 (the remainder is 0, so 3 and 1619 are divisors of 4857)
...
4857 / 68 = 71.426470588235 (the remainder is 29, so 68 is not a divisor of 4857)
4857 / 69 = 70.391304347826 (the remainder is 27, so 69 is not a divisor of 4857)