What are the divisors of 1882?

1, 2, 941, 1882

There is a total of 4 positive divisors.
The sum of these divisors is 2826.
The arithmetic mean is 706.5.

2 even divisors

2, 1882

2 odd divisors

1, 941

How to compute the divisors of 1882?

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 1882 by each of the numbers from 1 to 1882 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)

1882 / 1 = 1882 (the remainder is 0, so 1 is a divisor of 1882)
1882 / 2 = 941 (the remainder is 0, so 2 is a divisor of 1882)
1882 / 3 = 627.33333333333 (the remainder is 1, so 3 is not a divisor of 1882)
...
1882 / 1881 = 1.0005316321106 (the remainder is 1, so 1881 is not a divisor of 1882)
1882 / 1882 = 1 (the remainder is 0, so 1882 is a divisor of 1882)

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 1882 (i.e. 43.382023926968). 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 $\frac{N}{d} = D$ )

1882 / 1 = 1882 (the remainder is 0, so 1 and 1882 are divisors of 1882)
1882 / 2 = 941 (the remainder is 0, so 2 and 941 are divisors of 1882)
1882 / 3 = 627.33333333333 (the remainder is 1, so 3 is not a divisor of 1882)
...
1882 / 42 = 44.809523809524 (the remainder is 34, so 42 is not a divisor of 1882)
1882 / 43 = 43.767441860465 (the remainder is 33, so 43 is not a divisor of 1882)