What are the divisors of 2426?

1, 2, 1213, 2426

There is a total of 4 positive divisors.
The sum of these divisors is 3642.
The arithmetic mean is 910.5.

2 even divisors

2, 2426

2 odd divisors

1, 1213

How to compute the divisors of 2426?

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 2426 by each of the numbers from 1 to 2426 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)

2426 / 1 = 2426 (the remainder is 0, so 1 is a divisor of 2426)
2426 / 2 = 1213 (the remainder is 0, so 2 is a divisor of 2426)
2426 / 3 = 808.66666666667 (the remainder is 2, so 3 is not a divisor of 2426)
...
2426 / 2425 = 1.000412371134 (the remainder is 1, so 2425 is not a divisor of 2426)
2426 / 2426 = 1 (the remainder is 0, so 2426 is a divisor of 2426)

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 2426 (i.e. 49.254441424099). 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 $\frac{N}{d} = D$ )

2426 / 1 = 2426 (the remainder is 0, so 1 and 2426 are divisors of 2426)
2426 / 2 = 1213 (the remainder is 0, so 2 and 1213 are divisors of 2426)
2426 / 3 = 808.66666666667 (the remainder is 2, so 3 is not a divisor of 2426)
...
2426 / 48 = 50.541666666667 (the remainder is 26, so 48 is not a divisor of 2426)
2426 / 49 = 49.510204081633 (the remainder is 25, so 49 is not a divisor of 2426)