What are the divisors of 6091?

1, 6091

There is a total of 2 positive divisors.
The sum of these divisors is 6092.
The arithmetic mean is 3046.

2 odd divisors

1, 6091

How to compute the divisors of 6091?

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 6091 by each of the numbers from 1 to 6091 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)

6091 / 1 = 6091 (the remainder is 0, so 1 is a divisor of 6091)
6091 / 2 = 3045.5 (the remainder is 1, so 2 is not a divisor of 6091)
6091 / 3 = 2030.3333333333 (the remainder is 1, so 3 is not a divisor of 6091)
...
6091 / 6090 = 1.0001642036125 (the remainder is 1, so 6090 is not a divisor of 6091)
6091 / 6091 = 1 (the remainder is 0, so 6091 is a divisor of 6091)

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 6091 (i.e. 78.044858895381). 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 $\frac{N}{d} = D$ )

6091 / 1 = 6091 (the remainder is 0, so 1 and 6091 are divisors of 6091)
6091 / 2 = 3045.5 (the remainder is 1, so 2 is not a divisor of 6091)
6091 / 3 = 2030.3333333333 (the remainder is 1, so 3 is not a divisor of 6091)
...
6091 / 77 = 79.103896103896 (the remainder is 8, so 77 is not a divisor of 6091)
6091 / 78 = 78.089743589744 (the remainder is 7, so 78 is not a divisor of 6091)