What are the divisors of 2427?

1, 3, 809, 2427

There is a total of 4 positive divisors.
The sum of these divisors is 3240.
The arithmetic mean is 810.

4 odd divisors

1, 3, 809, 2427

How to compute the divisors of 2427?

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 2427 by each of the numbers from 1 to 2427 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)

2427 / 1 = 2427 (the remainder is 0, so 1 is a divisor of 2427)
2427 / 2 = 1213.5 (the remainder is 1, so 2 is not a divisor of 2427)
2427 / 3 = 809 (the remainder is 0, so 3 is a divisor of 2427)
...
2427 / 2426 = 1.0004122011542 (the remainder is 1, so 2426 is not a divisor of 2427)
2427 / 2427 = 1 (the remainder is 0, so 2427 is a divisor of 2427)

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 2427 (i.e. 49.264591747014). 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 $\frac{N}{d} = D$ )

2427 / 1 = 2427 (the remainder is 0, so 1 and 2427 are divisors of 2427)
2427 / 2 = 1213.5 (the remainder is 1, so 2 is not a divisor of 2427)
2427 / 3 = 809 (the remainder is 0, so 3 and 809 are divisors of 2427)
...
2427 / 48 = 50.5625 (the remainder is 27, so 48 is not a divisor of 2427)
2427 / 49 = 49.530612244898 (the remainder is 26, so 49 is not a divisor of 2427)