What are the divisors of 246?

1, 2, 3, 6, 41, 82, 123, 246

There is a total of 8 positive divisors.
The sum of these divisors is 504.
The arithmetic mean is 63.

4 even divisors

2, 6, 82, 246

4 odd divisors

1, 3, 41, 123

How to compute the divisors of 246?

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 246 by each of the numbers from 1 to 246 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)

246 / 1 = 246 (the remainder is 0, so 1 is a divisor of 246)
246 / 2 = 123 (the remainder is 0, so 2 is a divisor of 246)
246 / 3 = 82 (the remainder is 0, so 3 is a divisor of 246)
...
246 / 245 = 1.0040816326531 (the remainder is 1, so 245 is not a divisor of 246)
246 / 246 = 1 (the remainder is 0, so 246 is a divisor of 246)

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 246 (i.e. 15.684387141358). 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 $\frac{N}{d} = D$ )

246 / 1 = 246 (the remainder is 0, so 1 and 246 are divisors of 246)
246 / 2 = 123 (the remainder is 0, so 2 and 123 are divisors of 246)
246 / 3 = 82 (the remainder is 0, so 3 and 82 are divisors of 246)
...
246 / 14 = 17.571428571429 (the remainder is 8, so 14 is not a divisor of 246)
246 / 15 = 16.4 (the remainder is 6, so 15 is not a divisor of 246)