What are the divisors of 4814?

1, 2, 29, 58, 83, 166, 2407, 4814

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

4 even divisors

2, 58, 166, 4814

4 odd divisors

1, 29, 83, 2407

How to compute the divisors of 4814?

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 4814 by each of the numbers from 1 to 4814 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)

4814 / 1 = 4814 (the remainder is 0, so 1 is a divisor of 4814)
4814 / 2 = 2407 (the remainder is 0, so 2 is a divisor of 4814)
4814 / 3 = 1604.6666666667 (the remainder is 2, so 3 is not a divisor of 4814)
...
4814 / 4813 = 1.0002077706212 (the remainder is 1, so 4813 is not a divisor of 4814)
4814 / 4814 = 1 (the remainder is 0, so 4814 is a divisor of 4814)

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 4814 (i.e. 69.382995034807). 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 $\frac{N}{d} = D$ )

4814 / 1 = 4814 (the remainder is 0, so 1 and 4814 are divisors of 4814)
4814 / 2 = 2407 (the remainder is 0, so 2 and 2407 are divisors of 4814)
4814 / 3 = 1604.6666666667 (the remainder is 2, so 3 is not a divisor of 4814)
...
4814 / 68 = 70.794117647059 (the remainder is 54, so 68 is not a divisor of 4814)
4814 / 69 = 69.768115942029 (the remainder is 53, so 69 is not a divisor of 4814)