What are the divisors of 5677?

1, 7, 811, 5677

There is a total of 4 positive divisors.
The sum of these divisors is 6496.
The arithmetic mean is 1624.

4 odd divisors

1, 7, 811, 5677

How to compute the divisors of 5677?

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 5677 by each of the numbers from 1 to 5677 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)

5677 / 1 = 5677 (the remainder is 0, so 1 is a divisor of 5677)
5677 / 2 = 2838.5 (the remainder is 1, so 2 is not a divisor of 5677)
5677 / 3 = 1892.3333333333 (the remainder is 1, so 3 is not a divisor of 5677)
...
5677 / 5676 = 1.0001761804087 (the remainder is 1, so 5676 is not a divisor of 5677)
5677 / 5677 = 1 (the remainder is 0, so 5677 is a divisor of 5677)

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 5677 (i.e. 75.345869163478). 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 $\frac{N}{d} = D$ )

5677 / 1 = 5677 (the remainder is 0, so 1 and 5677 are divisors of 5677)
5677 / 2 = 2838.5 (the remainder is 1, so 2 is not a divisor of 5677)
5677 / 3 = 1892.3333333333 (the remainder is 1, so 3 is not a divisor of 5677)
...
5677 / 74 = 76.716216216216 (the remainder is 53, so 74 is not a divisor of 5677)
5677 / 75 = 75.693333333333 (the remainder is 52, so 75 is not a divisor of 5677)