What are the divisors of 6059?

1, 73, 83, 6059

There is a total of 4 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 1554.

4 odd divisors

1, 73, 83, 6059

How to compute the divisors of 6059?

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 6059 by each of the numbers from 1 to 6059 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)

6059 / 1 = 6059 (the remainder is 0, so 1 is a divisor of 6059)
6059 / 2 = 3029.5 (the remainder is 1, so 2 is not a divisor of 6059)
6059 / 3 = 2019.6666666667 (the remainder is 2, so 3 is not a divisor of 6059)
...
6059 / 6058 = 1.0001650709805 (the remainder is 1, so 6058 is not a divisor of 6059)
6059 / 6059 = 1 (the remainder is 0, so 6059 is a divisor of 6059)

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 6059 (i.e. 77.839578621675). 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 $\frac{N}{d} = D$ )

6059 / 1 = 6059 (the remainder is 0, so 1 and 6059 are divisors of 6059)
6059 / 2 = 3029.5 (the remainder is 1, so 2 is not a divisor of 6059)
6059 / 3 = 2019.6666666667 (the remainder is 2, so 3 is not a divisor of 6059)
...
6059 / 76 = 79.723684210526 (the remainder is 55, so 76 is not a divisor of 6059)
6059 / 77 = 78.688311688312 (the remainder is 53, so 77 is not a divisor of 6059)