What are the divisors of 5779?

1, 5779

There is a total of 2 positive divisors.
The sum of these divisors is 5780.
The arithmetic mean is 2890.

2 odd divisors

1, 5779

How to compute the divisors of 5779?

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 5779 by each of the numbers from 1 to 5779 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)

5779 / 1 = 5779 (the remainder is 0, so 1 is a divisor of 5779)
5779 / 2 = 2889.5 (the remainder is 1, so 2 is not a divisor of 5779)
5779 / 3 = 1926.3333333333 (the remainder is 1, so 3 is not a divisor of 5779)
...
5779 / 5778 = 1.0001730702665 (the remainder is 1, so 5778 is not a divisor of 5779)
5779 / 5779 = 1 (the remainder is 0, so 5779 is a divisor of 5779)

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 5779 (i.e. 76.019734279988). 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 $\frac{N}{d} = D$ )

5779 / 1 = 5779 (the remainder is 0, so 1 and 5779 are divisors of 5779)
5779 / 2 = 2889.5 (the remainder is 1, so 2 is not a divisor of 5779)
5779 / 3 = 1926.3333333333 (the remainder is 1, so 3 is not a divisor of 5779)
...
5779 / 75 = 77.053333333333 (the remainder is 4, so 75 is not a divisor of 5779)
5779 / 76 = 76.039473684211 (the remainder is 3, so 76 is not a divisor of 5779)