What are the divisors of 3017?

1, 7, 431, 3017

There is a total of 4 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 864.

4 odd divisors

1, 7, 431, 3017

How to compute the divisors of 3017?

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 3017 by each of the numbers from 1 to 3017 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)

3017 / 1 = 3017 (the remainder is 0, so 1 is a divisor of 3017)
3017 / 2 = 1508.5 (the remainder is 1, so 2 is not a divisor of 3017)
3017 / 3 = 1005.6666666667 (the remainder is 2, so 3 is not a divisor of 3017)
...
3017 / 3016 = 1.0003315649867 (the remainder is 1, so 3016 is not a divisor of 3017)
3017 / 3017 = 1 (the remainder is 0, so 3017 is a divisor of 3017)

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 3017 (i.e. 54.927224579438). 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 $\frac{N}{d} = D$ )

3017 / 1 = 3017 (the remainder is 0, so 1 and 3017 are divisors of 3017)
3017 / 2 = 1508.5 (the remainder is 1, so 2 is not a divisor of 3017)
3017 / 3 = 1005.6666666667 (the remainder is 2, so 3 is not a divisor of 3017)
...
3017 / 53 = 56.924528301887 (the remainder is 49, so 53 is not a divisor of 3017)
3017 / 54 = 55.87037037037 (the remainder is 47, so 54 is not a divisor of 3017)