What are the divisors of 2467?

1, 2467

There is a total of 2 positive divisors.
The sum of these divisors is 2468.
The arithmetic mean is 1234.

2 odd divisors

1, 2467

How to compute the divisors of 2467?

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 2467 by each of the numbers from 1 to 2467 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)

2467 / 1 = 2467 (the remainder is 0, so 1 is a divisor of 2467)
2467 / 2 = 1233.5 (the remainder is 1, so 2 is not a divisor of 2467)
2467 / 3 = 822.33333333333 (the remainder is 1, so 3 is not a divisor of 2467)
...
2467 / 2466 = 1.0004055150041 (the remainder is 1, so 2466 is not a divisor of 2467)
2467 / 2467 = 1 (the remainder is 0, so 2467 is a divisor of 2467)

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 2467 (i.e. 49.668903752751). 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 $\frac{N}{d} = D$ )

2467 / 1 = 2467 (the remainder is 0, so 1 and 2467 are divisors of 2467)
2467 / 2 = 1233.5 (the remainder is 1, so 2 is not a divisor of 2467)
2467 / 3 = 822.33333333333 (the remainder is 1, so 3 is not a divisor of 2467)
...
2467 / 48 = 51.395833333333 (the remainder is 19, so 48 is not a divisor of 2467)
2467 / 49 = 50.34693877551 (the remainder is 17, so 49 is not a divisor of 2467)