What are the divisors of 4724?

1, 2, 4, 1181, 2362, 4724

There is a total of 6 positive divisors.
The sum of these divisors is 8274.
The arithmetic mean is 1379.

4 even divisors

2, 4, 2362, 4724

2 odd divisors

1, 1181

How to compute the divisors of 4724?

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 4724 by each of the numbers from 1 to 4724 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)

4724 / 1 = 4724 (the remainder is 0, so 1 is a divisor of 4724)
4724 / 2 = 2362 (the remainder is 0, so 2 is a divisor of 4724)
4724 / 3 = 1574.6666666667 (the remainder is 2, so 3 is not a divisor of 4724)
...
4724 / 4723 = 1.0002117298327 (the remainder is 1, so 4723 is not a divisor of 4724)
4724 / 4724 = 1 (the remainder is 0, so 4724 is a divisor of 4724)

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 4724 (i.e. 68.731361109758). 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 $\frac{N}{d} = D$ )

4724 / 1 = 4724 (the remainder is 0, so 1 and 4724 are divisors of 4724)
4724 / 2 = 2362 (the remainder is 0, so 2 and 2362 are divisors of 4724)
4724 / 3 = 1574.6666666667 (the remainder is 2, so 3 is not a divisor of 4724)
...
4724 / 67 = 70.507462686567 (the remainder is 34, so 67 is not a divisor of 4724)
4724 / 68 = 69.470588235294 (the remainder is 32, so 68 is not a divisor of 4724)