What are the divisors of 1624?

1, 2, 4, 7, 8, 14, 28, 29, 56, 58, 116, 203, 232, 406, 812, 1624

There is a total of 16 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 225.

12 even divisors

2, 4, 8, 14, 28, 56, 58, 116, 232, 406, 812, 1624

4 odd divisors

1, 7, 29, 203

How to compute the divisors of 1624?

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 1624 by each of the numbers from 1 to 1624 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)

1624 / 1 = 1624 (the remainder is 0, so 1 is a divisor of 1624)
1624 / 2 = 812 (the remainder is 0, so 2 is a divisor of 1624)
1624 / 3 = 541.33333333333 (the remainder is 1, so 3 is not a divisor of 1624)
...
1624 / 1623 = 1.0006161429452 (the remainder is 1, so 1623 is not a divisor of 1624)
1624 / 1624 = 1 (the remainder is 0, so 1624 is a divisor of 1624)

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 1624 (i.e. 40.29888335922). 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 $\frac{N}{d} = D$ )

1624 / 1 = 1624 (the remainder is 0, so 1 and 1624 are divisors of 1624)
1624 / 2 = 812 (the remainder is 0, so 2 and 812 are divisors of 1624)
1624 / 3 = 541.33333333333 (the remainder is 1, so 3 is not a divisor of 1624)
...
1624 / 39 = 41.641025641026 (the remainder is 25, so 39 is not a divisor of 1624)
1624 / 40 = 40.6 (the remainder is 24, so 40 is not a divisor of 1624)