What are the divisors of 6042?

1, 2, 3, 6, 19, 38, 53, 57, 106, 114, 159, 318, 1007, 2014, 3021, 6042

There is a total of 16 positive divisors.
The sum of these divisors is 12960.
The arithmetic mean is 810.

8 even divisors

2, 6, 38, 106, 114, 318, 2014, 6042

8 odd divisors

1, 3, 19, 53, 57, 159, 1007, 3021

How to compute the divisors of 6042?

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 6042 by each of the numbers from 1 to 6042 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)

6042 / 1 = 6042 (the remainder is 0, so 1 is a divisor of 6042)
6042 / 2 = 3021 (the remainder is 0, so 2 is a divisor of 6042)
6042 / 3 = 2014 (the remainder is 0, so 3 is a divisor of 6042)
...
6042 / 6041 = 1.0001655355074 (the remainder is 1, so 6041 is not a divisor of 6042)
6042 / 6042 = 1 (the remainder is 0, so 6042 is a divisor of 6042)

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 6042 (i.e. 77.730302971235). 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 $\frac{N}{d} = D$ )

6042 / 1 = 6042 (the remainder is 0, so 1 and 6042 are divisors of 6042)
6042 / 2 = 3021 (the remainder is 0, so 2 and 3021 are divisors of 6042)
6042 / 3 = 2014 (the remainder is 0, so 3 and 2014 are divisors of 6042)
...
6042 / 76 = 79.5 (the remainder is 38, so 76 is not a divisor of 6042)
6042 / 77 = 78.467532467532 (the remainder is 36, so 77 is not a divisor of 6042)