What are the divisors of 1130?

1, 2, 5, 10, 113, 226, 565, 1130

There is a total of 8 positive divisors.
The sum of these divisors is 2052.
The arithmetic mean is 256.5.

4 even divisors

2, 10, 226, 1130

4 odd divisors

1, 5, 113, 565

How to compute the divisors of 1130?

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 1130 by each of the numbers from 1 to 1130 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)

1130 / 1 = 1130 (the remainder is 0, so 1 is a divisor of 1130)
1130 / 2 = 565 (the remainder is 0, so 2 is a divisor of 1130)
1130 / 3 = 376.66666666667 (the remainder is 2, so 3 is not a divisor of 1130)
...
1130 / 1129 = 1.0008857395926 (the remainder is 1, so 1129 is not a divisor of 1130)
1130 / 1130 = 1 (the remainder is 0, so 1130 is a divisor of 1130)

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 1130 (i.e. 33.615472627943). 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 $\frac{N}{d} = D$ )

1130 / 1 = 1130 (the remainder is 0, so 1 and 1130 are divisors of 1130)
1130 / 2 = 565 (the remainder is 0, so 2 and 565 are divisors of 1130)
1130 / 3 = 376.66666666667 (the remainder is 2, so 3 is not a divisor of 1130)
...
1130 / 32 = 35.3125 (the remainder is 10, so 32 is not a divisor of 1130)
1130 / 33 = 34.242424242424 (the remainder is 8, so 33 is not a divisor of 1130)