What are the divisors of 764?

1, 2, 4, 191, 382, 764

There is a total of 6 positive divisors.
The sum of these divisors is 1344.
The arithmetic mean is 224.

4 even divisors

2, 4, 382, 764

2 odd divisors

1, 191

How to compute the divisors of 764?

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 764 by each of the numbers from 1 to 764 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)

764 / 1 = 764 (the remainder is 0, so 1 is a divisor of 764)
764 / 2 = 382 (the remainder is 0, so 2 is a divisor of 764)
764 / 3 = 254.66666666667 (the remainder is 2, so 3 is not a divisor of 764)
...
764 / 763 = 1.0013106159895 (the remainder is 1, so 763 is not a divisor of 764)
764 / 764 = 1 (the remainder is 0, so 764 is a divisor of 764)

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 764 (i.e. 27.640549922171). 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 $\frac{N}{d} = D$ )

764 / 1 = 764 (the remainder is 0, so 1 and 764 are divisors of 764)
764 / 2 = 382 (the remainder is 0, so 2 and 382 are divisors of 764)
764 / 3 = 254.66666666667 (the remainder is 2, so 3 is not a divisor of 764)
...
764 / 26 = 29.384615384615 (the remainder is 10, so 26 is not a divisor of 764)
764 / 27 = 28.296296296296 (the remainder is 8, so 27 is not a divisor of 764)