What are the divisors of 2613?

1, 3, 13, 39, 67, 201, 871, 2613

There is a total of 8 positive divisors.
The sum of these divisors is 3808.
The arithmetic mean is 476.

8 odd divisors

1, 3, 13, 39, 67, 201, 871, 2613

How to compute the divisors of 2613?

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 2613 by each of the numbers from 1 to 2613 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)

2613 / 1 = 2613 (the remainder is 0, so 1 is a divisor of 2613)
2613 / 2 = 1306.5 (the remainder is 1, so 2 is not a divisor of 2613)
2613 / 3 = 871 (the remainder is 0, so 3 is a divisor of 2613)
...
2613 / 2612 = 1.000382848392 (the remainder is 1, so 2612 is not a divisor of 2613)
2613 / 2613 = 1 (the remainder is 0, so 2613 is a divisor of 2613)

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 2613 (i.e. 51.117511676528). 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 $\frac{N}{d} = D$ )

2613 / 1 = 2613 (the remainder is 0, so 1 and 2613 are divisors of 2613)
2613 / 2 = 1306.5 (the remainder is 1, so 2 is not a divisor of 2613)
2613 / 3 = 871 (the remainder is 0, so 3 and 871 are divisors of 2613)
...
2613 / 50 = 52.26 (the remainder is 13, so 50 is not a divisor of 2613)
2613 / 51 = 51.235294117647 (the remainder is 12, so 51 is not a divisor of 2613)