What are the divisors of 6061?

1, 11, 19, 29, 209, 319, 551, 6061

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

8 odd divisors

1, 11, 19, 29, 209, 319, 551, 6061

How to compute the divisors of 6061?

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 6061 by each of the numbers from 1 to 6061 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)

6061 / 1 = 6061 (the remainder is 0, so 1 is a divisor of 6061)
6061 / 2 = 3030.5 (the remainder is 1, so 2 is not a divisor of 6061)
6061 / 3 = 2020.3333333333 (the remainder is 1, so 3 is not a divisor of 6061)
...
6061 / 6060 = 1.0001650165017 (the remainder is 1, so 6060 is not a divisor of 6061)
6061 / 6061 = 1 (the remainder is 0, so 6061 is a divisor of 6061)

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 6061 (i.e. 77.852424496608). 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 $\frac{N}{d} = D$ )

6061 / 1 = 6061 (the remainder is 0, so 1 and 6061 are divisors of 6061)
6061 / 2 = 3030.5 (the remainder is 1, so 2 is not a divisor of 6061)
6061 / 3 = 2020.3333333333 (the remainder is 1, so 3 is not a divisor of 6061)
...
6061 / 76 = 79.75 (the remainder is 57, so 76 is not a divisor of 6061)
6061 / 77 = 78.714285714286 (the remainder is 55, so 77 is not a divisor of 6061)