What are the divisors of 4811?

1, 17, 283, 4811

There is a total of 4 positive divisors.
The sum of these divisors is 5112.
The arithmetic mean is 1278.

4 odd divisors

1, 17, 283, 4811

How to compute the divisors of 4811?

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 4811 by each of the numbers from 1 to 4811 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)

4811 / 1 = 4811 (the remainder is 0, so 1 is a divisor of 4811)
4811 / 2 = 2405.5 (the remainder is 1, so 2 is not a divisor of 4811)
4811 / 3 = 1603.6666666667 (the remainder is 2, so 3 is not a divisor of 4811)
...
4811 / 4810 = 1.0002079002079 (the remainder is 1, so 4810 is not a divisor of 4811)
4811 / 4811 = 1 (the remainder is 0, so 4811 is a divisor of 4811)

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 4811 (i.e. 69.361372535439). 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 $\frac{N}{d} = D$ )

4811 / 1 = 4811 (the remainder is 0, so 1 and 4811 are divisors of 4811)
4811 / 2 = 2405.5 (the remainder is 1, so 2 is not a divisor of 4811)
4811 / 3 = 1603.6666666667 (the remainder is 2, so 3 is not a divisor of 4811)
...
4811 / 68 = 70.75 (the remainder is 51, so 68 is not a divisor of 4811)
4811 / 69 = 69.724637681159 (the remainder is 50, so 69 is not a divisor of 4811)