What are the divisors of 2169?

1, 3, 9, 241, 723, 2169

There is a total of 6 positive divisors.
The sum of these divisors is 3146.
The arithmetic mean is 524.33333333333.

6 odd divisors

1, 3, 9, 241, 723, 2169

How to compute the divisors of 2169?

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 2169 by each of the numbers from 1 to 2169 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)

2169 / 1 = 2169 (the remainder is 0, so 1 is a divisor of 2169)
2169 / 2 = 1084.5 (the remainder is 1, so 2 is not a divisor of 2169)
2169 / 3 = 723 (the remainder is 0, so 3 is a divisor of 2169)
...
2169 / 2168 = 1.0004612546125 (the remainder is 1, so 2168 is not a divisor of 2169)
2169 / 2169 = 1 (the remainder is 0, so 2169 is a divisor of 2169)

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 2169 (i.e. 46.57252408878). 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 $\frac{N}{d} = D$ )

2169 / 1 = 2169 (the remainder is 0, so 1 and 2169 are divisors of 2169)
2169 / 2 = 1084.5 (the remainder is 1, so 2 is not a divisor of 2169)
2169 / 3 = 723 (the remainder is 0, so 3 and 723 are divisors of 2169)
...
2169 / 45 = 48.2 (the remainder is 9, so 45 is not a divisor of 2169)
2169 / 46 = 47.152173913043 (the remainder is 7, so 46 is not a divisor of 2169)