What are the divisors of 2764?

1, 2, 4, 691, 1382, 2764

There is a total of 6 positive divisors.
The sum of these divisors is 4844.
The arithmetic mean is 807.33333333333.

4 even divisors

2, 4, 1382, 2764

2 odd divisors

1, 691

How to compute the divisors of 2764?

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 2764 by each of the numbers from 1 to 2764 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)

2764 / 1 = 2764 (the remainder is 0, so 1 is a divisor of 2764)
2764 / 2 = 1382 (the remainder is 0, so 2 is a divisor of 2764)
2764 / 3 = 921.33333333333 (the remainder is 1, so 3 is not a divisor of 2764)
...
2764 / 2763 = 1.0003619254434 (the remainder is 1, so 2763 is not a divisor of 2764)
2764 / 2764 = 1 (the remainder is 0, so 2764 is a divisor of 2764)

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 2764 (i.e. 52.57375771238). 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 $\frac{N}{d} = D$ )

2764 / 1 = 2764 (the remainder is 0, so 1 and 2764 are divisors of 2764)
2764 / 2 = 1382 (the remainder is 0, so 2 and 1382 are divisors of 2764)
2764 / 3 = 921.33333333333 (the remainder is 1, so 3 is not a divisor of 2764)
...
2764 / 51 = 54.196078431373 (the remainder is 10, so 51 is not a divisor of 2764)
2764 / 52 = 53.153846153846 (the remainder is 8, so 52 is not a divisor of 2764)