What are the divisors of 2769?

1, 3, 13, 39, 71, 213, 923, 2769

There is a total of 8 positive divisors.
The sum of these divisors is 4032.
The arithmetic mean is 504.

8 odd divisors

1, 3, 13, 39, 71, 213, 923, 2769

How to compute the divisors of 2769?

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 2769 by each of the numbers from 1 to 2769 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)

2769 / 1 = 2769 (the remainder is 0, so 1 is a divisor of 2769)
2769 / 2 = 1384.5 (the remainder is 1, so 2 is not a divisor of 2769)
2769 / 3 = 923 (the remainder is 0, so 3 is a divisor of 2769)
...
2769 / 2768 = 1.0003612716763 (the remainder is 1, so 2768 is not a divisor of 2769)
2769 / 2769 = 1 (the remainder is 0, so 2769 is a divisor of 2769)

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 2769 (i.e. 52.621288467691). 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 $\frac{N}{d} = D$ )

2769 / 1 = 2769 (the remainder is 0, so 1 and 2769 are divisors of 2769)
2769 / 2 = 1384.5 (the remainder is 1, so 2 is not a divisor of 2769)
2769 / 3 = 923 (the remainder is 0, so 3 and 923 are divisors of 2769)
...
2769 / 51 = 54.294117647059 (the remainder is 15, so 51 is not a divisor of 2769)
2769 / 52 = 53.25 (the remainder is 13, so 52 is not a divisor of 2769)