What are the divisors of 779?

1, 19, 41, 779

There is a total of 4 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 210.

4 odd divisors

1, 19, 41, 779

How to compute the divisors of 779?

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 779 by each of the numbers from 1 to 779 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)

779 / 1 = 779 (the remainder is 0, so 1 is a divisor of 779)
779 / 2 = 389.5 (the remainder is 1, so 2 is not a divisor of 779)
779 / 3 = 259.66666666667 (the remainder is 2, so 3 is not a divisor of 779)
...
779 / 778 = 1.0012853470437 (the remainder is 1, so 778 is not a divisor of 779)
779 / 779 = 1 (the remainder is 0, so 779 is a divisor of 779)

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 779 (i.e. 27.910571473906). 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 $\frac{N}{d} = D$ )

779 / 1 = 779 (the remainder is 0, so 1 and 779 are divisors of 779)
779 / 2 = 389.5 (the remainder is 1, so 2 is not a divisor of 779)
779 / 3 = 259.66666666667 (the remainder is 2, so 3 is not a divisor of 779)
...
779 / 26 = 29.961538461538 (the remainder is 25, so 26 is not a divisor of 779)
779 / 27 = 28.851851851852 (the remainder is 23, so 27 is not a divisor of 779)