What are the divisors of 9042?

1, 2, 3, 6, 11, 22, 33, 66, 137, 274, 411, 822, 1507, 3014, 4521, 9042

There is a total of 16 positive divisors.
The sum of these divisors is 19872.
The arithmetic mean is 1242.

8 even divisors

2, 6, 22, 66, 274, 822, 3014, 9042

8 odd divisors

1, 3, 11, 33, 137, 411, 1507, 4521

How to compute the divisors of 9042?

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 9042 by each of the numbers from 1 to 9042 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)

9042 / 1 = 9042 (the remainder is 0, so 1 is a divisor of 9042)
9042 / 2 = 4521 (the remainder is 0, so 2 is a divisor of 9042)
9042 / 3 = 3014 (the remainder is 0, so 3 is a divisor of 9042)
...
9042 / 9041 = 1.0001106072337 (the remainder is 1, so 9041 is not a divisor of 9042)
9042 / 9042 = 1 (the remainder is 0, so 9042 is a divisor of 9042)

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 9042 (i.e. 95.089431589425). 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 $\frac{N}{d} = D$ )

9042 / 1 = 9042 (the remainder is 0, so 1 and 9042 are divisors of 9042)
9042 / 2 = 4521 (the remainder is 0, so 2 and 4521 are divisors of 9042)
9042 / 3 = 3014 (the remainder is 0, so 3 and 3014 are divisors of 9042)
...
9042 / 94 = 96.191489361702 (the remainder is 18, so 94 is not a divisor of 9042)
9042 / 95 = 95.178947368421 (the remainder is 17, so 95 is not a divisor of 9042)