What are the divisors of 2182?

1, 2, 1091, 2182

There is a total of 4 positive divisors.
The sum of these divisors is 3276.
The arithmetic mean is 819.

2 even divisors

2, 2182

2 odd divisors

1, 1091

How to compute the divisors of 2182?

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 2182 by each of the numbers from 1 to 2182 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)

2182 / 1 = 2182 (the remainder is 0, so 1 is a divisor of 2182)
2182 / 2 = 1091 (the remainder is 0, so 2 is a divisor of 2182)
2182 / 3 = 727.33333333333 (the remainder is 1, so 3 is not a divisor of 2182)
...
2182 / 2181 = 1.0004585052728 (the remainder is 1, so 2181 is not a divisor of 2182)
2182 / 2182 = 1 (the remainder is 0, so 2182 is a divisor of 2182)

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 2182 (i.e. 46.711882856507). 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 $\frac{N}{d} = D$ )

2182 / 1 = 2182 (the remainder is 0, so 1 and 2182 are divisors of 2182)
2182 / 2 = 1091 (the remainder is 0, so 2 and 1091 are divisors of 2182)
2182 / 3 = 727.33333333333 (the remainder is 1, so 3 is not a divisor of 2182)
...
2182 / 45 = 48.488888888889 (the remainder is 22, so 45 is not a divisor of 2182)
2182 / 46 = 47.434782608696 (the remainder is 20, so 46 is not a divisor of 2182)