What are the divisors of 4718?

1, 2, 7, 14, 337, 674, 2359, 4718

There is a total of 8 positive divisors.
The sum of these divisors is 8112.
The arithmetic mean is 1014.

4 even divisors

2, 14, 674, 4718

4 odd divisors

1, 7, 337, 2359

How to compute the divisors of 4718?

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 4718 by each of the numbers from 1 to 4718 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)

4718 / 1 = 4718 (the remainder is 0, so 1 is a divisor of 4718)
4718 / 2 = 2359 (the remainder is 0, so 2 is a divisor of 4718)
4718 / 3 = 1572.6666666667 (the remainder is 2, so 3 is not a divisor of 4718)
...
4718 / 4717 = 1.000211999152 (the remainder is 1, so 4717 is not a divisor of 4718)
4718 / 4718 = 1 (the remainder is 0, so 4718 is a divisor of 4718)

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 4718 (i.e. 68.687699044298). 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 $\frac{N}{d} = D$ )

4718 / 1 = 4718 (the remainder is 0, so 1 and 4718 are divisors of 4718)
4718 / 2 = 2359 (the remainder is 0, so 2 and 2359 are divisors of 4718)
4718 / 3 = 1572.6666666667 (the remainder is 2, so 3 is not a divisor of 4718)
...
4718 / 67 = 70.417910447761 (the remainder is 28, so 67 is not a divisor of 4718)
4718 / 68 = 69.382352941176 (the remainder is 26, so 68 is not a divisor of 4718)