What are the divisors of 4813?

1, 4813

There is a total of 2 positive divisors.
The sum of these divisors is 4814.
The arithmetic mean is 2407.

2 odd divisors

1, 4813

How to compute the divisors of 4813?

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 4813 by each of the numbers from 1 to 4813 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)

4813 / 1 = 4813 (the remainder is 0, so 1 is a divisor of 4813)
4813 / 2 = 2406.5 (the remainder is 1, so 2 is not a divisor of 4813)
4813 / 3 = 1604.3333333333 (the remainder is 1, so 3 is not a divisor of 4813)
...
4813 / 4812 = 1.0002078137988 (the remainder is 1, so 4812 is not a divisor of 4813)
4813 / 4813 = 1 (the remainder is 0, so 4813 is a divisor of 4813)

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 4813 (i.e. 69.37578828381). 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 $\frac{N}{d} = D$ )

4813 / 1 = 4813 (the remainder is 0, so 1 and 4813 are divisors of 4813)
4813 / 2 = 2406.5 (the remainder is 1, so 2 is not a divisor of 4813)
4813 / 3 = 1604.3333333333 (the remainder is 1, so 3 is not a divisor of 4813)
...
4813 / 68 = 70.779411764706 (the remainder is 53, so 68 is not a divisor of 4813)
4813 / 69 = 69.753623188406 (the remainder is 52, so 69 is not a divisor of 4813)