What are the divisors of 2759?

1, 31, 89, 2759

There is a total of 4 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 720.

4 odd divisors

1, 31, 89, 2759

How to compute the divisors of 2759?

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 2759 by each of the numbers from 1 to 2759 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)

2759 / 1 = 2759 (the remainder is 0, so 1 is a divisor of 2759)
2759 / 2 = 1379.5 (the remainder is 1, so 2 is not a divisor of 2759)
2759 / 3 = 919.66666666667 (the remainder is 2, so 3 is not a divisor of 2759)
...
2759 / 2758 = 1.0003625815809 (the remainder is 1, so 2758 is not a divisor of 2759)
2759 / 2759 = 1 (the remainder is 0, so 2759 is a divisor of 2759)

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 2759 (i.e. 52.526183946676). 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 $\frac{N}{d} = D$ )

2759 / 1 = 2759 (the remainder is 0, so 1 and 2759 are divisors of 2759)
2759 / 2 = 1379.5 (the remainder is 1, so 2 is not a divisor of 2759)
2759 / 3 = 919.66666666667 (the remainder is 2, so 3 is not a divisor of 2759)
...
2759 / 51 = 54.098039215686 (the remainder is 5, so 51 is not a divisor of 2759)
2759 / 52 = 53.057692307692 (the remainder is 3, so 52 is not a divisor of 2759)