What are the divisors of 2658?

1, 2, 3, 6, 443, 886, 1329, 2658

There is a total of 8 positive divisors.
The sum of these divisors is 5328.
The arithmetic mean is 666.

4 even divisors

2, 6, 886, 2658

4 odd divisors

1, 3, 443, 1329

How to compute the divisors of 2658?

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 2658 by each of the numbers from 1 to 2658 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)

2658 / 1 = 2658 (the remainder is 0, so 1 is a divisor of 2658)
2658 / 2 = 1329 (the remainder is 0, so 2 is a divisor of 2658)
2658 / 3 = 886 (the remainder is 0, so 3 is a divisor of 2658)
...
2658 / 2657 = 1.0003763643207 (the remainder is 1, so 2657 is not a divisor of 2658)
2658 / 2658 = 1 (the remainder is 0, so 2658 is a divisor of 2658)

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 2658 (i.e. 51.555795018601). 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 $\frac{N}{d} = D$ )

2658 / 1 = 2658 (the remainder is 0, so 1 and 2658 are divisors of 2658)
2658 / 2 = 1329 (the remainder is 0, so 2 and 1329 are divisors of 2658)
2658 / 3 = 886 (the remainder is 0, so 3 and 886 are divisors of 2658)
...
2658 / 50 = 53.16 (the remainder is 8, so 50 is not a divisor of 2658)
2658 / 51 = 52.117647058824 (the remainder is 6, so 51 is not a divisor of 2658)