What are the divisors of 2651?

1, 11, 241, 2651

There is a total of 4 positive divisors.
The sum of these divisors is 2904.
The arithmetic mean is 726.

4 odd divisors

1, 11, 241, 2651

How to compute the divisors of 2651?

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 2651 by each of the numbers from 1 to 2651 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)

2651 / 1 = 2651 (the remainder is 0, so 1 is a divisor of 2651)
2651 / 2 = 1325.5 (the remainder is 1, so 2 is not a divisor of 2651)
2651 / 3 = 883.66666666667 (the remainder is 2, so 3 is not a divisor of 2651)
...
2651 / 2650 = 1.0003773584906 (the remainder is 1, so 2650 is not a divisor of 2651)
2651 / 2651 = 1 (the remainder is 0, so 2651 is a divisor of 2651)

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 2651 (i.e. 51.487862647424). 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 $\frac{N}{d} = D$ )

2651 / 1 = 2651 (the remainder is 0, so 1 and 2651 are divisors of 2651)
2651 / 2 = 1325.5 (the remainder is 1, so 2 is not a divisor of 2651)
2651 / 3 = 883.66666666667 (the remainder is 2, so 3 is not a divisor of 2651)
...
2651 / 50 = 53.02 (the remainder is 1, so 50 is not a divisor of 2651)
2651 / 51 = 51.980392156863 (the remainder is 50, so 51 is not a divisor of 2651)