What are the divisors of 6141?

1, 3, 23, 69, 89, 267, 2047, 6141

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

8 odd divisors

1, 3, 23, 69, 89, 267, 2047, 6141

How to compute the divisors of 6141?

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 6141 by each of the numbers from 1 to 6141 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)

6141 / 1 = 6141 (the remainder is 0, so 1 is a divisor of 6141)
6141 / 2 = 3070.5 (the remainder is 1, so 2 is not a divisor of 6141)
6141 / 3 = 2047 (the remainder is 0, so 3 is a divisor of 6141)
...
6141 / 6140 = 1.0001628664495 (the remainder is 1, so 6140 is not a divisor of 6141)
6141 / 6141 = 1 (the remainder is 0, so 6141 is a divisor of 6141)

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 6141 (i.e. 78.36453279386). 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 $\frac{N}{d} = D$ )

6141 / 1 = 6141 (the remainder is 0, so 1 and 6141 are divisors of 6141)
6141 / 2 = 3070.5 (the remainder is 1, so 2 is not a divisor of 6141)
6141 / 3 = 2047 (the remainder is 0, so 3 and 2047 are divisors of 6141)
...
6141 / 77 = 79.753246753247 (the remainder is 58, so 77 is not a divisor of 6141)
6141 / 78 = 78.730769230769 (the remainder is 57, so 78 is not a divisor of 6141)