What are the divisors of 1150?

1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150

There is a total of 12 positive divisors.
The sum of these divisors is 2232.
The arithmetic mean is 186.

6 even divisors

2, 10, 46, 50, 230, 1150

6 odd divisors

1, 5, 23, 25, 115, 575

How to compute the divisors of 1150?

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 1150 by each of the numbers from 1 to 1150 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)

1150 / 1 = 1150 (the remainder is 0, so 1 is a divisor of 1150)
1150 / 2 = 575 (the remainder is 0, so 2 is a divisor of 1150)
1150 / 3 = 383.33333333333 (the remainder is 1, so 3 is not a divisor of 1150)
...
1150 / 1149 = 1.0008703220191 (the remainder is 1, so 1149 is not a divisor of 1150)
1150 / 1150 = 1 (the remainder is 0, so 1150 is a divisor of 1150)

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 1150 (i.e. 33.911649915626). 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 $\frac{N}{d} = D$ )

1150 / 1 = 1150 (the remainder is 0, so 1 and 1150 are divisors of 1150)
1150 / 2 = 575 (the remainder is 0, so 2 and 575 are divisors of 1150)
1150 / 3 = 383.33333333333 (the remainder is 1, so 3 is not a divisor of 1150)
...
1150 / 32 = 35.9375 (the remainder is 30, so 32 is not a divisor of 1150)
1150 / 33 = 34.848484848485 (the remainder is 28, so 33 is not a divisor of 1150)