What are the divisors of 2643?

1, 3, 881, 2643

There is a total of 4 positive divisors.
The sum of these divisors is 3528.
The arithmetic mean is 882.

4 odd divisors

1, 3, 881, 2643

How to compute the divisors of 2643?

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 2643 by each of the numbers from 1 to 2643 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)

2643 / 1 = 2643 (the remainder is 0, so 1 is a divisor of 2643)
2643 / 2 = 1321.5 (the remainder is 1, so 2 is not a divisor of 2643)
2643 / 3 = 881 (the remainder is 0, so 3 is a divisor of 2643)
...
2643 / 2642 = 1.0003785011355 (the remainder is 1, so 2642 is not a divisor of 2643)
2643 / 2643 = 1 (the remainder is 0, so 2643 is a divisor of 2643)

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 2643 (i.e. 51.410115736108). 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 $\frac{N}{d} = D$ )

2643 / 1 = 2643 (the remainder is 0, so 1 and 2643 are divisors of 2643)
2643 / 2 = 1321.5 (the remainder is 1, so 2 is not a divisor of 2643)
2643 / 3 = 881 (the remainder is 0, so 3 and 881 are divisors of 2643)
...
2643 / 50 = 52.86 (the remainder is 43, so 50 is not a divisor of 2643)
2643 / 51 = 51.823529411765 (the remainder is 42, so 51 is not a divisor of 2643)