What are the divisors of 1160?

1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, 1160

There is a total of 16 positive divisors.
The sum of these divisors is 2700.
The arithmetic mean is 168.75.

12 even divisors

2, 4, 8, 10, 20, 40, 58, 116, 232, 290, 580, 1160

4 odd divisors

1, 5, 29, 145

How to compute the divisors of 1160?

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 1160 by each of the numbers from 1 to 1160 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)

1160 / 1 = 1160 (the remainder is 0, so 1 is a divisor of 1160)
1160 / 2 = 580 (the remainder is 0, so 2 is a divisor of 1160)
1160 / 3 = 386.66666666667 (the remainder is 2, so 3 is not a divisor of 1160)
...
1160 / 1159 = 1.0008628127696 (the remainder is 1, so 1159 is not a divisor of 1160)
1160 / 1160 = 1 (the remainder is 0, so 1160 is a divisor of 1160)

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 1160 (i.e. 34.058772731853). 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 $\frac{N}{d} = D$ )

1160 / 1 = 1160 (the remainder is 0, so 1 and 1160 are divisors of 1160)
1160 / 2 = 580 (the remainder is 0, so 2 and 580 are divisors of 1160)
1160 / 3 = 386.66666666667 (the remainder is 2, so 3 is not a divisor of 1160)
...
1160 / 33 = 35.151515151515 (the remainder is 5, so 33 is not a divisor of 1160)
1160 / 34 = 34.117647058824 (the remainder is 4, so 34 is not a divisor of 1160)