What are the divisors of 2469?

1, 3, 823, 2469

There is a total of 4 positive divisors.
The sum of these divisors is 3296.
The arithmetic mean is 824.

4 odd divisors

1, 3, 823, 2469

How to compute the divisors of 2469?

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 2469 by each of the numbers from 1 to 2469 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)

2469 / 1 = 2469 (the remainder is 0, so 1 is a divisor of 2469)
2469 / 2 = 1234.5 (the remainder is 1, so 2 is not a divisor of 2469)
2469 / 3 = 823 (the remainder is 0, so 3 is a divisor of 2469)
...
2469 / 2468 = 1.0004051863857 (the remainder is 1, so 2468 is not a divisor of 2469)
2469 / 2469 = 1 (the remainder is 0, so 2469 is a divisor of 2469)

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 2469 (i.e. 49.689032995219). 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 $\frac{N}{d} = D$ )

2469 / 1 = 2469 (the remainder is 0, so 1 and 2469 are divisors of 2469)
2469 / 2 = 1234.5 (the remainder is 1, so 2 is not a divisor of 2469)
2469 / 3 = 823 (the remainder is 0, so 3 and 823 are divisors of 2469)
...
2469 / 48 = 51.4375 (the remainder is 21, so 48 is not a divisor of 2469)
2469 / 49 = 50.387755102041 (the remainder is 19, so 49 is not a divisor of 2469)