What are the divisors of 3031?

1, 7, 433, 3031

There is a total of 4 positive divisors.
The sum of these divisors is 3472.
The arithmetic mean is 868.

4 odd divisors

1, 7, 433, 3031

How to compute the divisors of 3031?

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 3031 by each of the numbers from 1 to 3031 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)

3031 / 1 = 3031 (the remainder is 0, so 1 is a divisor of 3031)
3031 / 2 = 1515.5 (the remainder is 1, so 2 is not a divisor of 3031)
3031 / 3 = 1010.3333333333 (the remainder is 1, so 3 is not a divisor of 3031)
...
3031 / 3030 = 1.0003300330033 (the remainder is 1, so 3030 is not a divisor of 3031)
3031 / 3031 = 1 (the remainder is 0, so 3031 is a divisor of 3031)

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 3031 (i.e. 55.054518434003). 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 $\frac{N}{d} = D$ )

3031 / 1 = 3031 (the remainder is 0, so 1 and 3031 are divisors of 3031)
3031 / 2 = 1515.5 (the remainder is 1, so 2 is not a divisor of 3031)
3031 / 3 = 1010.3333333333 (the remainder is 1, so 3 is not a divisor of 3031)
...
3031 / 54 = 56.12962962963 (the remainder is 7, so 54 is not a divisor of 3031)
3031 / 55 = 55.109090909091 (the remainder is 6, so 55 is not a divisor of 3031)