What are the divisors of 758?

1, 2, 379, 758

There is a total of 4 positive divisors.
The sum of these divisors is 1140.
The arithmetic mean is 285.

2 even divisors

2, 758

2 odd divisors

1, 379

How to compute the divisors of 758?

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 758 by each of the numbers from 1 to 758 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)

758 / 1 = 758 (the remainder is 0, so 1 is a divisor of 758)
758 / 2 = 379 (the remainder is 0, so 2 is a divisor of 758)
758 / 3 = 252.66666666667 (the remainder is 2, so 3 is not a divisor of 758)
...
758 / 757 = 1.001321003963 (the remainder is 1, so 757 is not a divisor of 758)
758 / 758 = 1 (the remainder is 0, so 758 is a divisor of 758)

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 758 (i.e. 27.531799795872). 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 $\frac{N}{d} = D$ )

758 / 1 = 758 (the remainder is 0, so 1 and 758 are divisors of 758)
758 / 2 = 379 (the remainder is 0, so 2 and 379 are divisors of 758)
758 / 3 = 252.66666666667 (the remainder is 2, so 3 is not a divisor of 758)
...
758 / 26 = 29.153846153846 (the remainder is 4, so 26 is not a divisor of 758)
758 / 27 = 28.074074074074 (the remainder is 2, so 27 is not a divisor of 758)