What are the divisors of 2611?

1, 7, 373, 2611

There is a total of 4 positive divisors.
The sum of these divisors is 2992.
The arithmetic mean is 748.

4 odd divisors

1, 7, 373, 2611

How to compute the divisors of 2611?

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 2611 by each of the numbers from 1 to 2611 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)

2611 / 1 = 2611 (the remainder is 0, so 1 is a divisor of 2611)
2611 / 2 = 1305.5 (the remainder is 1, so 2 is not a divisor of 2611)
2611 / 3 = 870.33333333333 (the remainder is 1, so 3 is not a divisor of 2611)
...
2611 / 2610 = 1.0003831417625 (the remainder is 1, so 2610 is not a divisor of 2611)
2611 / 2611 = 1 (the remainder is 0, so 2611 is a divisor of 2611)

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 2611 (i.e. 51.097945164165). 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 $\frac{N}{d} = D$ )

2611 / 1 = 2611 (the remainder is 0, so 1 and 2611 are divisors of 2611)
2611 / 2 = 1305.5 (the remainder is 1, so 2 is not a divisor of 2611)
2611 / 3 = 870.33333333333 (the remainder is 1, so 3 is not a divisor of 2611)
...
2611 / 50 = 52.22 (the remainder is 11, so 50 is not a divisor of 2611)
2611 / 51 = 51.196078431373 (the remainder is 10, so 51 is not a divisor of 2611)