What are the divisors of 2446?

1, 2, 1223, 2446

There is a total of 4 positive divisors.
The sum of these divisors is 3672.
The arithmetic mean is 918.

2 even divisors

2, 2446

2 odd divisors

1, 1223

How to compute the divisors of 2446?

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 2446 by each of the numbers from 1 to 2446 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)

2446 / 1 = 2446 (the remainder is 0, so 1 is a divisor of 2446)
2446 / 2 = 1223 (the remainder is 0, so 2 is a divisor of 2446)
2446 / 3 = 815.33333333333 (the remainder is 1, so 3 is not a divisor of 2446)
...
2446 / 2445 = 1.000408997955 (the remainder is 1, so 2445 is not a divisor of 2446)
2446 / 2446 = 1 (the remainder is 0, so 2446 is a divisor of 2446)

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 2446 (i.e. 49.457052075513). 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 $\frac{N}{d} = D$ )

2446 / 1 = 2446 (the remainder is 0, so 1 and 2446 are divisors of 2446)
2446 / 2 = 1223 (the remainder is 0, so 2 and 1223 are divisors of 2446)
2446 / 3 = 815.33333333333 (the remainder is 1, so 3 is not a divisor of 2446)
...
2446 / 48 = 50.958333333333 (the remainder is 46, so 48 is not a divisor of 2446)
2446 / 49 = 49.918367346939 (the remainder is 45, so 49 is not a divisor of 2446)