What are the divisors of 4688?

1, 2, 4, 8, 16, 293, 586, 1172, 2344, 4688

There is a total of 10 positive divisors.
The sum of these divisors is 9114.
The arithmetic mean is 911.4.

8 even divisors

2, 4, 8, 16, 586, 1172, 2344, 4688

2 odd divisors

1, 293

How to compute the divisors of 4688?

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 4688 by each of the numbers from 1 to 4688 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)

4688 / 1 = 4688 (the remainder is 0, so 1 is a divisor of 4688)
4688 / 2 = 2344 (the remainder is 0, so 2 is a divisor of 4688)
4688 / 3 = 1562.6666666667 (the remainder is 2, so 3 is not a divisor of 4688)
...
4688 / 4687 = 1.0002133560913 (the remainder is 1, so 4687 is not a divisor of 4688)
4688 / 4688 = 1 (the remainder is 0, so 4688 is a divisor of 4688)

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 4688 (i.e. 68.468971074495). 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 $\frac{N}{d} = D$ )

4688 / 1 = 4688 (the remainder is 0, so 1 and 4688 are divisors of 4688)
4688 / 2 = 2344 (the remainder is 0, so 2 and 2344 are divisors of 4688)
4688 / 3 = 1562.6666666667 (the remainder is 2, so 3 is not a divisor of 4688)
...
4688 / 67 = 69.970149253731 (the remainder is 65, so 67 is not a divisor of 4688)
4688 / 68 = 68.941176470588 (the remainder is 64, so 68 is not a divisor of 4688)