What are the divisors of 1011?

1, 3, 337, 1011

There is a total of 4 positive divisors.
The sum of these divisors is 1352.
The arithmetic mean is 338.

4 odd divisors

1, 3, 337, 1011

How to compute the divisors of 1011?

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 1011 by each of the numbers from 1 to 1011 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)

1011 / 1 = 1011 (the remainder is 0, so 1 is a divisor of 1011)
1011 / 2 = 505.5 (the remainder is 1, so 2 is not a divisor of 1011)
1011 / 3 = 337 (the remainder is 0, so 3 is a divisor of 1011)
...
1011 / 1010 = 1.0009900990099 (the remainder is 1, so 1010 is not a divisor of 1011)
1011 / 1011 = 1 (the remainder is 0, so 1011 is a divisor of 1011)

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 1011 (i.e. 31.796226191169). 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 $\frac{N}{d} = D$ )

1011 / 1 = 1011 (the remainder is 0, so 1 and 1011 are divisors of 1011)
1011 / 2 = 505.5 (the remainder is 1, so 2 is not a divisor of 1011)
1011 / 3 = 337 (the remainder is 0, so 3 and 337 are divisors of 1011)
...
1011 / 30 = 33.7 (the remainder is 21, so 30 is not a divisor of 1011)
1011 / 31 = 32.612903225806 (the remainder is 19, so 31 is not a divisor of 1011)