What are the divisors of 2623?

1, 43, 61, 2623

There is a total of 4 positive divisors.
The sum of these divisors is 2728.
The arithmetic mean is 682.

4 odd divisors

1, 43, 61, 2623

How to compute the divisors of 2623?

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 2623 by each of the numbers from 1 to 2623 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)

2623 / 1 = 2623 (the remainder is 0, so 1 is a divisor of 2623)
2623 / 2 = 1311.5 (the remainder is 1, so 2 is not a divisor of 2623)
2623 / 3 = 874.33333333333 (the remainder is 1, so 3 is not a divisor of 2623)
...
2623 / 2622 = 1.0003813882532 (the remainder is 1, so 2622 is not a divisor of 2623)
2623 / 2623 = 1 (the remainder is 0, so 2623 is a divisor of 2623)

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 2623 (i.e. 51.215232109208). 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 $\frac{N}{d} = D$ )

2623 / 1 = 2623 (the remainder is 0, so 1 and 2623 are divisors of 2623)
2623 / 2 = 1311.5 (the remainder is 1, so 2 is not a divisor of 2623)
2623 / 3 = 874.33333333333 (the remainder is 1, so 3 is not a divisor of 2623)
...
2623 / 50 = 52.46 (the remainder is 23, so 50 is not a divisor of 2623)
2623 / 51 = 51.43137254902 (the remainder is 22, so 51 is not a divisor of 2623)