What are the divisors of 2466?

1, 2, 3, 6, 9, 18, 137, 274, 411, 822, 1233, 2466

There is a total of 12 positive divisors.
The sum of these divisors is 5382.
The arithmetic mean is 448.5.

6 even divisors

2, 6, 18, 274, 822, 2466

6 odd divisors

1, 3, 9, 137, 411, 1233

How to compute the divisors of 2466?

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 2466 by each of the numbers from 1 to 2466 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)

2466 / 1 = 2466 (the remainder is 0, so 1 is a divisor of 2466)
2466 / 2 = 1233 (the remainder is 0, so 2 is a divisor of 2466)
2466 / 3 = 822 (the remainder is 0, so 3 is a divisor of 2466)
...
2466 / 2465 = 1.0004056795132 (the remainder is 1, so 2465 is not a divisor of 2466)
2466 / 2466 = 1 (the remainder is 0, so 2466 is a divisor of 2466)

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 2466 (i.e. 49.658836071741). 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 $\frac{N}{d} = D$ )

2466 / 1 = 2466 (the remainder is 0, so 1 and 2466 are divisors of 2466)
2466 / 2 = 1233 (the remainder is 0, so 2 and 1233 are divisors of 2466)
2466 / 3 = 822 (the remainder is 0, so 3 and 822 are divisors of 2466)
...
2466 / 48 = 51.375 (the remainder is 18, so 48 is not a divisor of 2466)
2466 / 49 = 50.326530612245 (the remainder is 16, so 49 is not a divisor of 2466)