What are the divisors of 1868?

1, 2, 4, 467, 934, 1868

There is a total of 6 positive divisors.
The sum of these divisors is 3276.
The arithmetic mean is 546.

4 even divisors

2, 4, 934, 1868

2 odd divisors

1, 467

How to compute the divisors of 1868?

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 1868 by each of the numbers from 1 to 1868 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)

1868 / 1 = 1868 (the remainder is 0, so 1 is a divisor of 1868)
1868 / 2 = 934 (the remainder is 0, so 2 is a divisor of 1868)
1868 / 3 = 622.66666666667 (the remainder is 2, so 3 is not a divisor of 1868)
...
1868 / 1867 = 1.0005356186395 (the remainder is 1, so 1867 is not a divisor of 1868)
1868 / 1868 = 1 (the remainder is 0, so 1868 is a divisor of 1868)

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 1868 (i.e. 43.220365569949). 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 $\frac{N}{d} = D$ )

1868 / 1 = 1868 (the remainder is 0, so 1 and 1868 are divisors of 1868)
1868 / 2 = 934 (the remainder is 0, so 2 and 934 are divisors of 1868)
1868 / 3 = 622.66666666667 (the remainder is 2, so 3 is not a divisor of 1868)
...
1868 / 42 = 44.47619047619 (the remainder is 20, so 42 is not a divisor of 1868)
1868 / 43 = 43.441860465116 (the remainder is 19, so 43 is not a divisor of 1868)