What are the divisors of 6021?

1, 3, 9, 27, 223, 669, 2007, 6021

There is a total of 8 positive divisors.
The sum of these divisors is 8960.
The arithmetic mean is 1120.

8 odd divisors

1, 3, 9, 27, 223, 669, 2007, 6021

How to compute the divisors of 6021?

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 6021 by each of the numbers from 1 to 6021 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)

6021 / 1 = 6021 (the remainder is 0, so 1 is a divisor of 6021)
6021 / 2 = 3010.5 (the remainder is 1, so 2 is not a divisor of 6021)
6021 / 3 = 2007 (the remainder is 0, so 3 is a divisor of 6021)
...
6021 / 6020 = 1.0001661129568 (the remainder is 1, so 6020 is not a divisor of 6021)
6021 / 6021 = 1 (the remainder is 0, so 6021 is a divisor of 6021)

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 6021 (i.e. 77.595102938265). 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 $\frac{N}{d} = D$ )

6021 / 1 = 6021 (the remainder is 0, so 1 and 6021 are divisors of 6021)
6021 / 2 = 3010.5 (the remainder is 1, so 2 is not a divisor of 6021)
6021 / 3 = 2007 (the remainder is 0, so 3 and 2007 are divisors of 6021)
...
6021 / 76 = 79.223684210526 (the remainder is 17, so 76 is not a divisor of 6021)
6021 / 77 = 78.194805194805 (the remainder is 15, so 77 is not a divisor of 6021)