What are the divisors of 2381?

1, 2381

There is a total of 2 positive divisors.
The sum of these divisors is 2382.
The arithmetic mean is 1191.

2 odd divisors

1, 2381

How to compute the divisors of 2381?

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 2381 by each of the numbers from 1 to 2381 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)

2381 / 1 = 2381 (the remainder is 0, so 1 is a divisor of 2381)
2381 / 2 = 1190.5 (the remainder is 1, so 2 is not a divisor of 2381)
2381 / 3 = 793.66666666667 (the remainder is 2, so 3 is not a divisor of 2381)
...
2381 / 2380 = 1.0004201680672 (the remainder is 1, so 2380 is not a divisor of 2381)
2381 / 2381 = 1 (the remainder is 0, so 2381 is a divisor of 2381)

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 2381 (i.e. 48.795491595023). 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 $\frac{N}{d} = D$ )

2381 / 1 = 2381 (the remainder is 0, so 1 and 2381 are divisors of 2381)
2381 / 2 = 1190.5 (the remainder is 1, so 2 is not a divisor of 2381)
2381 / 3 = 793.66666666667 (the remainder is 2, so 3 is not a divisor of 2381)
...
2381 / 47 = 50.659574468085 (the remainder is 31, so 47 is not a divisor of 2381)
2381 / 48 = 49.604166666667 (the remainder is 29, so 48 is not a divisor of 2381)