What are the divisors of 2061?

1, 3, 9, 229, 687, 2061

There is a total of 6 positive divisors.
The sum of these divisors is 2990.
The arithmetic mean is 498.33333333333.

6 odd divisors

1, 3, 9, 229, 687, 2061

How to compute the divisors of 2061?

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 2061 by each of the numbers from 1 to 2061 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)

2061 / 1 = 2061 (the remainder is 0, so 1 is a divisor of 2061)
2061 / 2 = 1030.5 (the remainder is 1, so 2 is not a divisor of 2061)
2061 / 3 = 687 (the remainder is 0, so 3 is a divisor of 2061)
...
2061 / 2060 = 1.0004854368932 (the remainder is 1, so 2060 is not a divisor of 2061)
2061 / 2061 = 1 (the remainder is 0, so 2061 is a divisor of 2061)

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 2061 (i.e. 45.398237851265). 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 $\frac{N}{d} = D$ )

2061 / 1 = 2061 (the remainder is 0, so 1 and 2061 are divisors of 2061)
2061 / 2 = 1030.5 (the remainder is 1, so 2 is not a divisor of 2061)
2061 / 3 = 687 (the remainder is 0, so 3 and 687 are divisors of 2061)
...
2061 / 44 = 46.840909090909 (the remainder is 37, so 44 is not a divisor of 2061)
2061 / 45 = 45.8 (the remainder is 36, so 45 is not a divisor of 2061)