What are the divisors of 2124?

1, 2, 3, 4, 6, 9, 12, 18, 36, 59, 118, 177, 236, 354, 531, 708, 1062, 2124

There is a total of 18 positive divisors.
The sum of these divisors is 5460.
The arithmetic mean is 303.33333333333.

12 even divisors

2, 4, 6, 12, 18, 36, 118, 236, 354, 708, 1062, 2124

6 odd divisors

1, 3, 9, 59, 177, 531

How to compute the divisors of 2124?

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 2124 by each of the numbers from 1 to 2124 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)

2124 / 1 = 2124 (the remainder is 0, so 1 is a divisor of 2124)
2124 / 2 = 1062 (the remainder is 0, so 2 is a divisor of 2124)
2124 / 3 = 708 (the remainder is 0, so 3 is a divisor of 2124)
...
2124 / 2123 = 1.0004710315591 (the remainder is 1, so 2123 is not a divisor of 2124)
2124 / 2124 = 1 (the remainder is 0, so 2124 is a divisor of 2124)

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 2124 (i.e. 46.086874487212). 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 $\frac{N}{d} = D$ )

2124 / 1 = 2124 (the remainder is 0, so 1 and 2124 are divisors of 2124)
2124 / 2 = 1062 (the remainder is 0, so 2 and 1062 are divisors of 2124)
2124 / 3 = 708 (the remainder is 0, so 3 and 708 are divisors of 2124)
...
2124 / 45 = 47.2 (the remainder is 9, so 45 is not a divisor of 2124)
2124 / 46 = 46.173913043478 (the remainder is 8, so 46 is not a divisor of 2124)