What are the divisors of 7074?

1, 2, 3, 6, 9, 18, 27, 54, 131, 262, 393, 786, 1179, 2358, 3537, 7074

There is a total of 16 positive divisors.
The sum of these divisors is 15840.
The arithmetic mean is 990.

8 even divisors

2, 6, 18, 54, 262, 786, 2358, 7074

8 odd divisors

1, 3, 9, 27, 131, 393, 1179, 3537

How to compute the divisors of 7074?

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 7074 by each of the numbers from 1 to 7074 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)

7074 / 1 = 7074 (the remainder is 0, so 1 is a divisor of 7074)
7074 / 2 = 3537 (the remainder is 0, so 2 is a divisor of 7074)
7074 / 3 = 2358 (the remainder is 0, so 3 is a divisor of 7074)
...
7074 / 7073 = 1.000141382723 (the remainder is 1, so 7073 is not a divisor of 7074)
7074 / 7074 = 1 (the remainder is 0, so 7074 is a divisor of 7074)

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 7074 (i.e. 84.107074613257). 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 $\frac{N}{d} = D$ )

7074 / 1 = 7074 (the remainder is 0, so 1 and 7074 are divisors of 7074)
7074 / 2 = 3537 (the remainder is 0, so 2 and 3537 are divisors of 7074)
7074 / 3 = 2358 (the remainder is 0, so 3 and 2358 are divisors of 7074)
...
7074 / 83 = 85.228915662651 (the remainder is 19, so 83 is not a divisor of 7074)
7074 / 84 = 84.214285714286 (the remainder is 18, so 84 is not a divisor of 7074)