What are the divisors of 6031?

1, 37, 163, 6031

There is a total of 4 positive divisors.
The sum of these divisors is 6232.
The arithmetic mean is 1558.

4 odd divisors

1, 37, 163, 6031

How to compute the divisors of 6031?

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 6031 by each of the numbers from 1 to 6031 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)

6031 / 1 = 6031 (the remainder is 0, so 1 is a divisor of 6031)
6031 / 2 = 3015.5 (the remainder is 1, so 2 is not a divisor of 6031)
6031 / 3 = 2010.3333333333 (the remainder is 1, so 3 is not a divisor of 6031)
...
6031 / 6030 = 1.0001658374793 (the remainder is 1, so 6030 is not a divisor of 6031)
6031 / 6031 = 1 (the remainder is 0, so 6031 is a divisor of 6031)

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 6031 (i.e. 77.659513261416). 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 $\frac{N}{d} = D$ )

6031 / 1 = 6031 (the remainder is 0, so 1 and 6031 are divisors of 6031)
6031 / 2 = 3015.5 (the remainder is 1, so 2 is not a divisor of 6031)
6031 / 3 = 2010.3333333333 (the remainder is 1, so 3 is not a divisor of 6031)
...
6031 / 76 = 79.355263157895 (the remainder is 27, so 76 is not a divisor of 6031)
6031 / 77 = 78.324675324675 (the remainder is 25, so 77 is not a divisor of 6031)