What are the divisors of 5767?

1, 73, 79, 5767

There is a total of 4 positive divisors.
The sum of these divisors is 5920.
The arithmetic mean is 1480.

4 odd divisors

1, 73, 79, 5767

How to compute the divisors of 5767?

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 5767 by each of the numbers from 1 to 5767 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)

5767 / 1 = 5767 (the remainder is 0, so 1 is a divisor of 5767)
5767 / 2 = 2883.5 (the remainder is 1, so 2 is not a divisor of 5767)
5767 / 3 = 1922.3333333333 (the remainder is 1, so 3 is not a divisor of 5767)
...
5767 / 5766 = 1.0001734304544 (the remainder is 1, so 5766 is not a divisor of 5767)
5767 / 5767 = 1 (the remainder is 0, so 5767 is a divisor of 5767)

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 5767 (i.e. 75.940766390655). 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 $\frac{N}{d} = D$ )

5767 / 1 = 5767 (the remainder is 0, so 1 and 5767 are divisors of 5767)
5767 / 2 = 2883.5 (the remainder is 1, so 2 is not a divisor of 5767)
5767 / 3 = 1922.3333333333 (the remainder is 1, so 3 is not a divisor of 5767)
...
5767 / 74 = 77.932432432432 (the remainder is 69, so 74 is not a divisor of 5767)
5767 / 75 = 76.893333333333 (the remainder is 67, so 75 is not a divisor of 5767)