What are the divisors of 769?

1, 769

There is a total of 2 positive divisors.
The sum of these divisors is 770.
The arithmetic mean is 385.

2 odd divisors

1, 769

How to compute the divisors of 769?

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 769 by each of the numbers from 1 to 769 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)

769 / 1 = 769 (the remainder is 0, so 1 is a divisor of 769)
769 / 2 = 384.5 (the remainder is 1, so 2 is not a divisor of 769)
769 / 3 = 256.33333333333 (the remainder is 1, so 3 is not a divisor of 769)
...
769 / 768 = 1.0013020833333 (the remainder is 1, so 768 is not a divisor of 769)
769 / 769 = 1 (the remainder is 0, so 769 is a divisor of 769)

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 769 (i.e. 27.730849247724). 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 $\frac{N}{d} = D$ )

769 / 1 = 769 (the remainder is 0, so 1 and 769 are divisors of 769)
769 / 2 = 384.5 (the remainder is 1, so 2 is not a divisor of 769)
769 / 3 = 256.33333333333 (the remainder is 1, so 3 is not a divisor of 769)
...
769 / 26 = 29.576923076923 (the remainder is 15, so 26 is not a divisor of 769)
769 / 27 = 28.481481481481 (the remainder is 13, so 27 is not a divisor of 769)