What are the divisors of 844?

1, 2, 4, 211, 422, 844

There is a total of 6 positive divisors.
The sum of these divisors is 1484.
The arithmetic mean is 247.33333333333.

4 even divisors

2, 4, 422, 844

2 odd divisors

1, 211

How to compute the divisors of 844?

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 844 by each of the numbers from 1 to 844 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)

844 / 1 = 844 (the remainder is 0, so 1 is a divisor of 844)
844 / 2 = 422 (the remainder is 0, so 2 is a divisor of 844)
844 / 3 = 281.33333333333 (the remainder is 1, so 3 is not a divisor of 844)
...
844 / 843 = 1.0011862396204 (the remainder is 1, so 843 is not a divisor of 844)
844 / 844 = 1 (the remainder is 0, so 844 is a divisor of 844)

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 844 (i.e. 29.051678092668). 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 $\frac{N}{d} = D$ )

844 / 1 = 844 (the remainder is 0, so 1 and 844 are divisors of 844)
844 / 2 = 422 (the remainder is 0, so 2 and 422 are divisors of 844)
844 / 3 = 281.33333333333 (the remainder is 1, so 3 is not a divisor of 844)
...
844 / 28 = 30.142857142857 (the remainder is 4, so 28 is not a divisor of 844)
844 / 29 = 29.103448275862 (the remainder is 3, so 29 is not a divisor of 844)