What are the divisors of 2347?

1, 2347

There is a total of 2 positive divisors.
The sum of these divisors is 2348.
The arithmetic mean is 1174.

2 odd divisors

1, 2347

How to compute the divisors of 2347?

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 2347 by each of the numbers from 1 to 2347 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)

2347 / 1 = 2347 (the remainder is 0, so 1 is a divisor of 2347)
2347 / 2 = 1173.5 (the remainder is 1, so 2 is not a divisor of 2347)
2347 / 3 = 782.33333333333 (the remainder is 1, so 3 is not a divisor of 2347)
...
2347 / 2346 = 1.0004262574595 (the remainder is 1, so 2346 is not a divisor of 2347)
2347 / 2347 = 1 (the remainder is 0, so 2347 is a divisor of 2347)

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 2347 (i.e. 48.445846055157). 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 $\frac{N}{d} = D$ )

2347 / 1 = 2347 (the remainder is 0, so 1 and 2347 are divisors of 2347)
2347 / 2 = 1173.5 (the remainder is 1, so 2 is not a divisor of 2347)
2347 / 3 = 782.33333333333 (the remainder is 1, so 3 is not a divisor of 2347)
...
2347 / 47 = 49.936170212766 (the remainder is 44, so 47 is not a divisor of 2347)
2347 / 48 = 48.895833333333 (the remainder is 43, so 48 is not a divisor of 2347)