What are the divisors of 1017?

1, 3, 9, 113, 339, 1017

There is a total of 6 positive divisors.
The sum of these divisors is 1482.
The arithmetic mean is 247.

6 odd divisors

1, 3, 9, 113, 339, 1017

How to compute the divisors of 1017?

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 1017 by each of the numbers from 1 to 1017 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)

1017 / 1 = 1017 (the remainder is 0, so 1 is a divisor of 1017)
1017 / 2 = 508.5 (the remainder is 1, so 2 is not a divisor of 1017)
1017 / 3 = 339 (the remainder is 0, so 3 is a divisor of 1017)
...
1017 / 1016 = 1.0009842519685 (the remainder is 1, so 1016 is not a divisor of 1017)
1017 / 1017 = 1 (the remainder is 0, so 1017 is a divisor of 1017)

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 1017 (i.e. 31.890437438204). 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 $\frac{N}{d} = D$ )

1017 / 1 = 1017 (the remainder is 0, so 1 and 1017 are divisors of 1017)
1017 / 2 = 508.5 (the remainder is 1, so 2 is not a divisor of 1017)
1017 / 3 = 339 (the remainder is 0, so 3 and 339 are divisors of 1017)
...
1017 / 30 = 33.9 (the remainder is 27, so 30 is not a divisor of 1017)
1017 / 31 = 32.806451612903 (the remainder is 25, so 31 is not a divisor of 1017)