What are the divisors of 778?

1, 2, 389, 778

There is a total of 4 positive divisors.
The sum of these divisors is 1170.
The arithmetic mean is 292.5.

2 even divisors

2, 778

2 odd divisors

1, 389

How to compute the divisors of 778?

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 778 by each of the numbers from 1 to 778 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)

778 / 1 = 778 (the remainder is 0, so 1 is a divisor of 778)
778 / 2 = 389 (the remainder is 0, so 2 is a divisor of 778)
778 / 3 = 259.33333333333 (the remainder is 1, so 3 is not a divisor of 778)
...
778 / 777 = 1.001287001287 (the remainder is 1, so 777 is not a divisor of 778)
778 / 778 = 1 (the remainder is 0, so 778 is a divisor of 778)

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 778 (i.e. 27.892651361963). 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 $\frac{N}{d} = D$ )

778 / 1 = 778 (the remainder is 0, so 1 and 778 are divisors of 778)
778 / 2 = 389 (the remainder is 0, so 2 and 389 are divisors of 778)
778 / 3 = 259.33333333333 (the remainder is 1, so 3 is not a divisor of 778)
...
778 / 26 = 29.923076923077 (the remainder is 24, so 26 is not a divisor of 778)
778 / 27 = 28.814814814815 (the remainder is 22, so 27 is not a divisor of 778)