What are the divisors of 774?

1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774

There is a total of 12 positive divisors.
The sum of these divisors is 1716.
The arithmetic mean is 143.

6 even divisors

2, 6, 18, 86, 258, 774

6 odd divisors

1, 3, 9, 43, 129, 387

How to compute the divisors of 774?

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 774 by each of the numbers from 1 to 774 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)

774 / 1 = 774 (the remainder is 0, so 1 is a divisor of 774)
774 / 2 = 387 (the remainder is 0, so 2 is a divisor of 774)
774 / 3 = 258 (the remainder is 0, so 3 is a divisor of 774)
...
774 / 773 = 1.0012936610608 (the remainder is 1, so 773 is not a divisor of 774)
774 / 774 = 1 (the remainder is 0, so 774 is a divisor of 774)

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 774 (i.e. 27.820855486487). 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 $\frac{N}{d} = D$ )

774 / 1 = 774 (the remainder is 0, so 1 and 774 are divisors of 774)
774 / 2 = 387 (the remainder is 0, so 2 and 387 are divisors of 774)
774 / 3 = 258 (the remainder is 0, so 3 and 258 are divisors of 774)
...
774 / 26 = 29.769230769231 (the remainder is 20, so 26 is not a divisor of 774)
774 / 27 = 28.666666666667 (the remainder is 18, so 27 is not a divisor of 774)