What are the divisors of 2423?

1, 2423

There is a total of 2 positive divisors.
The sum of these divisors is 2424.
The arithmetic mean is 1212.

2 odd divisors

1, 2423

How to compute the divisors of 2423?

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 2423 by each of the numbers from 1 to 2423 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)

2423 / 1 = 2423 (the remainder is 0, so 1 is a divisor of 2423)
2423 / 2 = 1211.5 (the remainder is 1, so 2 is not a divisor of 2423)
2423 / 3 = 807.66666666667 (the remainder is 2, so 3 is not a divisor of 2423)
...
2423 / 2422 = 1.0004128819158 (the remainder is 1, so 2422 is not a divisor of 2423)
2423 / 2423 = 1 (the remainder is 0, so 2423 is a divisor of 2423)

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 2423 (i.e. 49.223977896956). 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 $\frac{N}{d} = D$ )

2423 / 1 = 2423 (the remainder is 0, so 1 and 2423 are divisors of 2423)
2423 / 2 = 1211.5 (the remainder is 1, so 2 is not a divisor of 2423)
2423 / 3 = 807.66666666667 (the remainder is 2, so 3 is not a divisor of 2423)
...
2423 / 48 = 50.479166666667 (the remainder is 23, so 48 is not a divisor of 2423)
2423 / 49 = 49.448979591837 (the remainder is 22, so 49 is not a divisor of 2423)