What are the divisors of 2606?

1, 2, 1303, 2606

There is a total of 4 positive divisors.
The sum of these divisors is 3912.
The arithmetic mean is 978.

2 even divisors

2, 2606

2 odd divisors

1, 1303

How to compute the divisors of 2606?

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 2606 by each of the numbers from 1 to 2606 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)

2606 / 1 = 2606 (the remainder is 0, so 1 is a divisor of 2606)
2606 / 2 = 1303 (the remainder is 0, so 2 is a divisor of 2606)
2606 / 3 = 868.66666666667 (the remainder is 2, so 3 is not a divisor of 2606)
...
2606 / 2605 = 1.0003838771593 (the remainder is 1, so 2605 is not a divisor of 2606)
2606 / 2606 = 1 (the remainder is 0, so 2606 is a divisor of 2606)

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 2606 (i.e. 51.048996072401). 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 $\frac{N}{d} = D$ )

2606 / 1 = 2606 (the remainder is 0, so 1 and 2606 are divisors of 2606)
2606 / 2 = 1303 (the remainder is 0, so 2 and 1303 are divisors of 2606)
2606 / 3 = 868.66666666667 (the remainder is 2, so 3 is not a divisor of 2606)
...
2606 / 50 = 52.12 (the remainder is 6, so 50 is not a divisor of 2606)
2606 / 51 = 51.098039215686 (the remainder is 5, so 51 is not a divisor of 2606)