What are the divisors of 2628?

1, 2, 3, 4, 6, 9, 12, 18, 36, 73, 146, 219, 292, 438, 657, 876, 1314, 2628

There is a total of 18 positive divisors.
The sum of these divisors is 6734.
The arithmetic mean is 374.11111111111.

12 even divisors

2, 4, 6, 12, 18, 36, 146, 292, 438, 876, 1314, 2628

6 odd divisors

1, 3, 9, 73, 219, 657

How to compute the divisors of 2628?

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 2628 by each of the numbers from 1 to 2628 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)

2628 / 1 = 2628 (the remainder is 0, so 1 is a divisor of 2628)
2628 / 2 = 1314 (the remainder is 0, so 2 is a divisor of 2628)
2628 / 3 = 876 (the remainder is 0, so 3 is a divisor of 2628)
...
2628 / 2627 = 1.0003806623525 (the remainder is 1, so 2627 is not a divisor of 2628)
2628 / 2628 = 1 (the remainder is 0, so 2628 is a divisor of 2628)

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 2628 (i.e. 51.264022471905). 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 $\frac{N}{d} = D$ )

2628 / 1 = 2628 (the remainder is 0, so 1 and 2628 are divisors of 2628)
2628 / 2 = 1314 (the remainder is 0, so 2 and 1314 are divisors of 2628)
2628 / 3 = 876 (the remainder is 0, so 3 and 876 are divisors of 2628)
...
2628 / 50 = 52.56 (the remainder is 28, so 50 is not a divisor of 2628)
2628 / 51 = 51.529411764706 (the remainder is 27, so 51 is not a divisor of 2628)