What are the divisors of 757?

1, 757

There is a total of 2 positive divisors.
The sum of these divisors is 758.
The arithmetic mean is 379.

2 odd divisors

1, 757

How to compute the divisors of 757?

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 757 by each of the numbers from 1 to 757 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)

757 / 1 = 757 (the remainder is 0, so 1 is a divisor of 757)
757 / 2 = 378.5 (the remainder is 1, so 2 is not a divisor of 757)
757 / 3 = 252.33333333333 (the remainder is 1, so 3 is not a divisor of 757)
...
757 / 756 = 1.0013227513228 (the remainder is 1, so 756 is not a divisor of 757)
757 / 757 = 1 (the remainder is 0, so 757 is a divisor of 757)

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 757 (i.e. 27.513632984395). 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 $\frac{N}{d} = D$ )

757 / 1 = 757 (the remainder is 0, so 1 and 757 are divisors of 757)
757 / 2 = 378.5 (the remainder is 1, so 2 is not a divisor of 757)
757 / 3 = 252.33333333333 (the remainder is 1, so 3 is not a divisor of 757)
...
757 / 26 = 29.115384615385 (the remainder is 3, so 26 is not a divisor of 757)
757 / 27 = 28.037037037037 (the remainder is 1, so 27 is not a divisor of 757)