What are the divisors of 4684?

1, 2, 4, 1171, 2342, 4684

There is a total of 6 positive divisors.
The sum of these divisors is 8204.
The arithmetic mean is 1367.3333333333.

4 even divisors

2, 4, 2342, 4684

2 odd divisors

1, 1171

How to compute the divisors of 4684?

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 4684 by each of the numbers from 1 to 4684 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)

4684 / 1 = 4684 (the remainder is 0, so 1 is a divisor of 4684)
4684 / 2 = 2342 (the remainder is 0, so 2 is a divisor of 4684)
4684 / 3 = 1561.3333333333 (the remainder is 1, so 3 is not a divisor of 4684)
...
4684 / 4683 = 1.0002135383301 (the remainder is 1, so 4683 is not a divisor of 4684)
4684 / 4684 = 1 (the remainder is 0, so 4684 is a divisor of 4684)

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 4684 (i.e. 68.439754529075). 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 $\frac{N}{d} = D$ )

4684 / 1 = 4684 (the remainder is 0, so 1 and 4684 are divisors of 4684)
4684 / 2 = 2342 (the remainder is 0, so 2 and 2342 are divisors of 4684)
4684 / 3 = 1561.3333333333 (the remainder is 1, so 3 is not a divisor of 4684)
...
4684 / 67 = 69.910447761194 (the remainder is 61, so 67 is not a divisor of 4684)
4684 / 68 = 68.882352941176 (the remainder is 60, so 68 is not a divisor of 4684)