What are the divisors of 1869?

1, 3, 7, 21, 89, 267, 623, 1869

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

8 odd divisors

1, 3, 7, 21, 89, 267, 623, 1869

How to compute the divisors of 1869?

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 1869 by each of the numbers from 1 to 1869 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)

1869 / 1 = 1869 (the remainder is 0, so 1 is a divisor of 1869)
1869 / 2 = 934.5 (the remainder is 1, so 2 is not a divisor of 1869)
1869 / 3 = 623 (the remainder is 0, so 3 is a divisor of 1869)
...
1869 / 1868 = 1.0005353319058 (the remainder is 1, so 1868 is not a divisor of 1869)
1869 / 1869 = 1 (the remainder is 0, so 1869 is a divisor of 1869)

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 1869 (i.e. 43.231932642435). 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 $\frac{N}{d} = D$ )

1869 / 1 = 1869 (the remainder is 0, so 1 and 1869 are divisors of 1869)
1869 / 2 = 934.5 (the remainder is 1, so 2 is not a divisor of 1869)
1869 / 3 = 623 (the remainder is 0, so 3 and 623 are divisors of 1869)
...
1869 / 42 = 44.5 (the remainder is 21, so 42 is not a divisor of 1869)
1869 / 43 = 43.46511627907 (the remainder is 20, so 43 is not a divisor of 1869)