What are the divisors of 846?

1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846

There is a total of 12 positive divisors.
The sum of these divisors is 1872.
The arithmetic mean is 156.

6 even divisors

2, 6, 18, 94, 282, 846

6 odd divisors

1, 3, 9, 47, 141, 423

How to compute the divisors of 846?

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 846 by each of the numbers from 1 to 846 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)

846 / 1 = 846 (the remainder is 0, so 1 is a divisor of 846)
846 / 2 = 423 (the remainder is 0, so 2 is a divisor of 846)
846 / 3 = 282 (the remainder is 0, so 3 is a divisor of 846)
...
846 / 845 = 1.0011834319527 (the remainder is 1, so 845 is not a divisor of 846)
846 / 846 = 1 (the remainder is 0, so 846 is a divisor of 846)

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 846 (i.e. 29.086079144498). 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 $\frac{N}{d} = D$ )

846 / 1 = 846 (the remainder is 0, so 1 and 846 are divisors of 846)
846 / 2 = 423 (the remainder is 0, so 2 and 423 are divisors of 846)
846 / 3 = 282 (the remainder is 0, so 3 and 282 are divisors of 846)
...
846 / 28 = 30.214285714286 (the remainder is 6, so 28 is not a divisor of 846)
846 / 29 = 29.172413793103 (the remainder is 5, so 29 is not a divisor of 846)