What are the divisors of 2723?

1, 7, 389, 2723

There is a total of 4 positive divisors.
The sum of these divisors is 3120.
The arithmetic mean is 780.

4 odd divisors

1, 7, 389, 2723

How to compute the divisors of 2723?

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 2723 by each of the numbers from 1 to 2723 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)

2723 / 1 = 2723 (the remainder is 0, so 1 is a divisor of 2723)
2723 / 2 = 1361.5 (the remainder is 1, so 2 is not a divisor of 2723)
2723 / 3 = 907.66666666667 (the remainder is 2, so 3 is not a divisor of 2723)
...
2723 / 2722 = 1.0003673769287 (the remainder is 1, so 2722 is not a divisor of 2723)
2723 / 2723 = 1 (the remainder is 0, so 2723 is a divisor of 2723)

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 2723 (i.e. 52.182372502599). 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 $\frac{N}{d} = D$ )

2723 / 1 = 2723 (the remainder is 0, so 1 and 2723 are divisors of 2723)
2723 / 2 = 1361.5 (the remainder is 1, so 2 is not a divisor of 2723)
2723 / 3 = 907.66666666667 (the remainder is 2, so 3 is not a divisor of 2723)
...
2723 / 51 = 53.392156862745 (the remainder is 20, so 51 is not a divisor of 2723)
2723 / 52 = 52.365384615385 (the remainder is 19, so 52 is not a divisor of 2723)