What are the divisors of 759?

1, 3, 11, 23, 33, 69, 253, 759

There is a total of 8 positive divisors.
The sum of these divisors is 1152.
The arithmetic mean is 144.

8 odd divisors

1, 3, 11, 23, 33, 69, 253, 759

How to compute the divisors of 759?

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 759 by each of the numbers from 1 to 759 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)

759 / 1 = 759 (the remainder is 0, so 1 is a divisor of 759)
759 / 2 = 379.5 (the remainder is 1, so 2 is not a divisor of 759)
759 / 3 = 253 (the remainder is 0, so 3 is a divisor of 759)
...
759 / 758 = 1.0013192612137 (the remainder is 1, so 758 is not a divisor of 759)
759 / 759 = 1 (the remainder is 0, so 759 is a divisor of 759)

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 759 (i.e. 27.549954627912). 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 $\frac{N}{d} = D$ )

759 / 1 = 759 (the remainder is 0, so 1 and 759 are divisors of 759)
759 / 2 = 379.5 (the remainder is 1, so 2 is not a divisor of 759)
759 / 3 = 253 (the remainder is 0, so 3 and 253 are divisors of 759)
...
759 / 26 = 29.192307692308 (the remainder is 5, so 26 is not a divisor of 759)
759 / 27 = 28.111111111111 (the remainder is 3, so 27 is not a divisor of 759)