What are the divisors of 2371?

1, 2371

There is a total of 2 positive divisors.
The sum of these divisors is 2372.
The arithmetic mean is 1186.

2 odd divisors

1, 2371

How to compute the divisors of 2371?

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 2371 by each of the numbers from 1 to 2371 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)

2371 / 1 = 2371 (the remainder is 0, so 1 is a divisor of 2371)
2371 / 2 = 1185.5 (the remainder is 1, so 2 is not a divisor of 2371)
2371 / 3 = 790.33333333333 (the remainder is 1, so 3 is not a divisor of 2371)
...
2371 / 2370 = 1.0004219409283 (the remainder is 1, so 2370 is not a divisor of 2371)
2371 / 2371 = 1 (the remainder is 0, so 2371 is a divisor of 2371)

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 2371 (i.e. 48.692915295759). 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 $\frac{N}{d} = D$ )

2371 / 1 = 2371 (the remainder is 0, so 1 and 2371 are divisors of 2371)
2371 / 2 = 1185.5 (the remainder is 1, so 2 is not a divisor of 2371)
2371 / 3 = 790.33333333333 (the remainder is 1, so 3 is not a divisor of 2371)
...
2371 / 47 = 50.446808510638 (the remainder is 21, so 47 is not a divisor of 2371)
2371 / 48 = 49.395833333333 (the remainder is 19, so 48 is not a divisor of 2371)