What are the divisors of 2659?

1, 2659

There is a total of 2 positive divisors.
The sum of these divisors is 2660.
The arithmetic mean is 1330.

2 odd divisors

1, 2659

How to compute the divisors of 2659?

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 2659 by each of the numbers from 1 to 2659 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)

2659 / 1 = 2659 (the remainder is 0, so 1 is a divisor of 2659)
2659 / 2 = 1329.5 (the remainder is 1, so 2 is not a divisor of 2659)
2659 / 3 = 886.33333333333 (the remainder is 1, so 3 is not a divisor of 2659)
...
2659 / 2658 = 1.0003762227239 (the remainder is 1, so 2658 is not a divisor of 2659)
2659 / 2659 = 1 (the remainder is 0, so 2659 is a divisor of 2659)

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 2659 (i.e. 51.565492337415). 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 $\frac{N}{d} = D$ )

2659 / 1 = 2659 (the remainder is 0, so 1 and 2659 are divisors of 2659)
2659 / 2 = 1329.5 (the remainder is 1, so 2 is not a divisor of 2659)
2659 / 3 = 886.33333333333 (the remainder is 1, so 3 is not a divisor of 2659)
...
2659 / 50 = 53.18 (the remainder is 9, so 50 is not a divisor of 2659)
2659 / 51 = 52.137254901961 (the remainder is 7, so 51 is not a divisor of 2659)