What are the divisors of 860?

1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860

There is a total of 12 positive divisors.
The sum of these divisors is 1848.
The arithmetic mean is 154.

8 even divisors

2, 4, 10, 20, 86, 172, 430, 860

4 odd divisors

1, 5, 43, 215

How to compute the divisors of 860?

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 860 by each of the numbers from 1 to 860 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)

860 / 1 = 860 (the remainder is 0, so 1 is a divisor of 860)
860 / 2 = 430 (the remainder is 0, so 2 is a divisor of 860)
860 / 3 = 286.66666666667 (the remainder is 2, so 3 is not a divisor of 860)
...
860 / 859 = 1.0011641443539 (the remainder is 1, so 859 is not a divisor of 860)
860 / 860 = 1 (the remainder is 0, so 860 is a divisor of 860)

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 860 (i.e. 29.32575659723). 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 $\frac{N}{d} = D$ )

860 / 1 = 860 (the remainder is 0, so 1 and 860 are divisors of 860)
860 / 2 = 430 (the remainder is 0, so 2 and 430 are divisors of 860)
860 / 3 = 286.66666666667 (the remainder is 2, so 3 is not a divisor of 860)
...
860 / 28 = 30.714285714286 (the remainder is 20, so 28 is not a divisor of 860)
860 / 29 = 29.655172413793 (the remainder is 19, so 29 is not a divisor of 860)