What are the divisors of 4624?

1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, 4624

There is a total of 15 positive divisors.
The sum of these divisors is 9517.
The arithmetic mean is 634.46666666667.

12 even divisors

2, 4, 8, 16, 34, 68, 136, 272, 578, 1156, 2312, 4624

3 odd divisors

1, 17, 289

How to compute the divisors of 4624?

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 4624 by each of the numbers from 1 to 4624 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)

4624 / 1 = 4624 (the remainder is 0, so 1 is a divisor of 4624)
4624 / 2 = 2312 (the remainder is 0, so 2 is a divisor of 4624)
4624 / 3 = 1541.3333333333 (the remainder is 1, so 3 is not a divisor of 4624)
...
4624 / 4623 = 1.0002163097556 (the remainder is 1, so 4623 is not a divisor of 4624)
4624 / 4624 = 1 (the remainder is 0, so 4624 is a divisor of 4624)

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 4624 (i.e. 68). 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 $\frac{N}{d} = D$ )

4624 / 1 = 4624 (the remainder is 0, so 1 and 4624 are divisors of 4624)
4624 / 2 = 2312 (the remainder is 0, so 2 and 2312 are divisors of 4624)
4624 / 3 = 1541.3333333333 (the remainder is 1, so 3 is not a divisor of 4624)
...
4624 / 67 = 69.014925373134 (the remainder is 1, so 67 is not a divisor of 4624)
4624 / 68 = 68 (the remainder is 0, so 68 and 68 are divisors of 4624)