What are the divisors of 2601?

1, 3, 9, 17, 51, 153, 289, 867, 2601

There is a total of 9 positive divisors.
The sum of these divisors is 3991.
The arithmetic mean is 443.44444444444.

9 odd divisors

1, 3, 9, 17, 51, 153, 289, 867, 2601

How to compute the divisors of 2601?

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 2601 by each of the numbers from 1 to 2601 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)

2601 / 1 = 2601 (the remainder is 0, so 1 is a divisor of 2601)
2601 / 2 = 1300.5 (the remainder is 1, so 2 is not a divisor of 2601)
2601 / 3 = 867 (the remainder is 0, so 3 is a divisor of 2601)
...
2601 / 2600 = 1.0003846153846 (the remainder is 1, so 2600 is not a divisor of 2601)
2601 / 2601 = 1 (the remainder is 0, so 2601 is a divisor of 2601)

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 2601 (i.e. 51). 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 $\frac{N}{d} = D$ )

2601 / 1 = 2601 (the remainder is 0, so 1 and 2601 are divisors of 2601)
2601 / 2 = 1300.5 (the remainder is 1, so 2 is not a divisor of 2601)
2601 / 3 = 867 (the remainder is 0, so 3 and 867 are divisors of 2601)
...
2601 / 50 = 52.02 (the remainder is 1, so 50 is not a divisor of 2601)
2601 / 51 = 51 (the remainder is 0, so 51 and 51 are divisors of 2601)