What are the divisors of 2673?

1, 3, 9, 11, 27, 33, 81, 99, 243, 297, 891, 2673

There is a total of 12 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 364.

12 odd divisors

1, 3, 9, 11, 27, 33, 81, 99, 243, 297, 891, 2673

How to compute the divisors of 2673?

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 2673 by each of the numbers from 1 to 2673 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)

2673 / 1 = 2673 (the remainder is 0, so 1 is a divisor of 2673)
2673 / 2 = 1336.5 (the remainder is 1, so 2 is not a divisor of 2673)
2673 / 3 = 891 (the remainder is 0, so 3 is a divisor of 2673)
...
2673 / 2672 = 1.000374251497 (the remainder is 1, so 2672 is not a divisor of 2673)
2673 / 2673 = 1 (the remainder is 0, so 2673 is a divisor of 2673)

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 2673 (i.e. 51.701063818842). 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 $\frac{N}{d} = D$ )

2673 / 1 = 2673 (the remainder is 0, so 1 and 2673 are divisors of 2673)
2673 / 2 = 1336.5 (the remainder is 1, so 2 is not a divisor of 2673)
2673 / 3 = 891 (the remainder is 0, so 3 and 891 are divisors of 2673)
...
2673 / 50 = 53.46 (the remainder is 23, so 50 is not a divisor of 2673)
2673 / 51 = 52.411764705882 (the remainder is 21, so 51 is not a divisor of 2673)