What are the divisors of 9140?

1, 2, 4, 5, 10, 20, 457, 914, 1828, 2285, 4570, 9140

There is a total of 12 positive divisors.
The sum of these divisors is 19236.
The arithmetic mean is 1603.

8 even divisors

2, 4, 10, 20, 914, 1828, 4570, 9140

4 odd divisors

1, 5, 457, 2285

How to compute the divisors of 9140?

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 9140 by each of the numbers from 1 to 9140 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)

9140 / 1 = 9140 (the remainder is 0, so 1 is a divisor of 9140)
9140 / 2 = 4570 (the remainder is 0, so 2 is a divisor of 9140)
9140 / 3 = 3046.6666666667 (the remainder is 2, so 3 is not a divisor of 9140)
...
9140 / 9139 = 1.0001094211621 (the remainder is 1, so 9139 is not a divisor of 9140)
9140 / 9140 = 1 (the remainder is 0, so 9140 is a divisor of 9140)

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 9140 (i.e. 95.603347221737). 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 $\frac{N}{d} = D$ )

9140 / 1 = 9140 (the remainder is 0, so 1 and 9140 are divisors of 9140)
9140 / 2 = 4570 (the remainder is 0, so 2 and 4570 are divisors of 9140)
9140 / 3 = 3046.6666666667 (the remainder is 2, so 3 is not a divisor of 9140)
...
9140 / 94 = 97.234042553191 (the remainder is 22, so 94 is not a divisor of 9140)
9140 / 95 = 96.210526315789 (the remainder is 20, so 95 is not a divisor of 9140)