What are the divisors of 2768?

1, 2, 4, 8, 16, 173, 346, 692, 1384, 2768

There is a total of 10 positive divisors.
The sum of these divisors is 5394.
The arithmetic mean is 539.4.

8 even divisors

2, 4, 8, 16, 346, 692, 1384, 2768

2 odd divisors

1, 173

How to compute the divisors of 2768?

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 2768 by each of the numbers from 1 to 2768 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)

2768 / 1 = 2768 (the remainder is 0, so 1 is a divisor of 2768)
2768 / 2 = 1384 (the remainder is 0, so 2 is a divisor of 2768)
2768 / 3 = 922.66666666667 (the remainder is 2, so 3 is not a divisor of 2768)
...
2768 / 2767 = 1.0003614022407 (the remainder is 1, so 2767 is not a divisor of 2768)
2768 / 2768 = 1 (the remainder is 0, so 2768 is a divisor of 2768)

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 2768 (i.e. 52.611785751864). 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 $\frac{N}{d} = D$ )

2768 / 1 = 2768 (the remainder is 0, so 1 and 2768 are divisors of 2768)
2768 / 2 = 1384 (the remainder is 0, so 2 and 1384 are divisors of 2768)
2768 / 3 = 922.66666666667 (the remainder is 2, so 3 is not a divisor of 2768)
...
2768 / 51 = 54.274509803922 (the remainder is 14, so 51 is not a divisor of 2768)
2768 / 52 = 53.230769230769 (the remainder is 12, so 52 is not a divisor of 2768)