What are the divisors of 2793?

1, 3, 7, 19, 21, 49, 57, 133, 147, 399, 931, 2793

There is a total of 12 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 380.

12 odd divisors

1, 3, 7, 19, 21, 49, 57, 133, 147, 399, 931, 2793

How to compute the divisors of 2793?

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 2793 by each of the numbers from 1 to 2793 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)

2793 / 1 = 2793 (the remainder is 0, so 1 is a divisor of 2793)
2793 / 2 = 1396.5 (the remainder is 1, so 2 is not a divisor of 2793)
2793 / 3 = 931 (the remainder is 0, so 3 is a divisor of 2793)
...
2793 / 2792 = 1.0003581661891 (the remainder is 1, so 2792 is not a divisor of 2793)
2793 / 2793 = 1 (the remainder is 0, so 2793 is a divisor of 2793)

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 2793 (i.e. 52.848841046895). 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 $\frac{N}{d} = D$ )

2793 / 1 = 2793 (the remainder is 0, so 1 and 2793 are divisors of 2793)
2793 / 2 = 1396.5 (the remainder is 1, so 2 is not a divisor of 2793)
2793 / 3 = 931 (the remainder is 0, so 3 and 931 are divisors of 2793)
...
2793 / 51 = 54.764705882353 (the remainder is 39, so 51 is not a divisor of 2793)
2793 / 52 = 53.711538461538 (the remainder is 37, so 52 is not a divisor of 2793)