What are the divisors of 6181?

1, 7, 883, 6181

There is a total of 4 positive divisors.
The sum of these divisors is 7072.
The arithmetic mean is 1768.

4 odd divisors

1, 7, 883, 6181

How to compute the divisors of 6181?

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 6181 by each of the numbers from 1 to 6181 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)

6181 / 1 = 6181 (the remainder is 0, so 1 is a divisor of 6181)
6181 / 2 = 3090.5 (the remainder is 1, so 2 is not a divisor of 6181)
6181 / 3 = 2060.3333333333 (the remainder is 1, so 3 is not a divisor of 6181)
...
6181 / 6180 = 1.0001618122977 (the remainder is 1, so 6180 is not a divisor of 6181)
6181 / 6181 = 1 (the remainder is 0, so 6181 is a divisor of 6181)

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 6181 (i.e. 78.619336044004). 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 $\frac{N}{d} = D$ )

6181 / 1 = 6181 (the remainder is 0, so 1 and 6181 are divisors of 6181)
6181 / 2 = 3090.5 (the remainder is 1, so 2 is not a divisor of 6181)
6181 / 3 = 2060.3333333333 (the remainder is 1, so 3 is not a divisor of 6181)
...
6181 / 77 = 80.272727272727 (the remainder is 21, so 77 is not a divisor of 6181)
6181 / 78 = 79.24358974359 (the remainder is 19, so 78 is not a divisor of 6181)