What are the divisors of 776?

1, 2, 4, 8, 97, 194, 388, 776

There is a total of 8 positive divisors.
The sum of these divisors is 1470.
The arithmetic mean is 183.75.

6 even divisors

2, 4, 8, 194, 388, 776

2 odd divisors

1, 97

How to compute the divisors of 776?

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 776 by each of the numbers from 1 to 776 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)

776 / 1 = 776 (the remainder is 0, so 1 is a divisor of 776)
776 / 2 = 388 (the remainder is 0, so 2 is a divisor of 776)
776 / 3 = 258.66666666667 (the remainder is 2, so 3 is not a divisor of 776)
...
776 / 775 = 1.0012903225806 (the remainder is 1, so 775 is not a divisor of 776)
776 / 776 = 1 (the remainder is 0, so 776 is a divisor of 776)

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 776 (i.e. 27.856776554368). 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 $\frac{N}{d} = D$ )

776 / 1 = 776 (the remainder is 0, so 1 and 776 are divisors of 776)
776 / 2 = 388 (the remainder is 0, so 2 and 388 are divisors of 776)
776 / 3 = 258.66666666667 (the remainder is 2, so 3 is not a divisor of 776)
...
776 / 26 = 29.846153846154 (the remainder is 22, so 26 is not a divisor of 776)
776 / 27 = 28.740740740741 (the remainder is 20, so 27 is not a divisor of 776)