What are the divisors of 7026?

1, 2, 3, 6, 1171, 2342, 3513, 7026

There is a total of 8 positive divisors.
The sum of these divisors is 14064.
The arithmetic mean is 1758.

4 even divisors

2, 6, 2342, 7026

4 odd divisors

1, 3, 1171, 3513

How to compute the divisors of 7026?

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 7026 by each of the numbers from 1 to 7026 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)

7026 / 1 = 7026 (the remainder is 0, so 1 is a divisor of 7026)
7026 / 2 = 3513 (the remainder is 0, so 2 is a divisor of 7026)
7026 / 3 = 2342 (the remainder is 0, so 3 is a divisor of 7026)
...
7026 / 7025 = 1.0001423487544 (the remainder is 1, so 7025 is not a divisor of 7026)
7026 / 7026 = 1 (the remainder is 0, so 7026 is a divisor of 7026)

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 7026 (i.e. 83.821238358784). 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 $\frac{N}{d} = D$ )

7026 / 1 = 7026 (the remainder is 0, so 1 and 7026 are divisors of 7026)
7026 / 2 = 3513 (the remainder is 0, so 2 and 3513 are divisors of 7026)
7026 / 3 = 2342 (the remainder is 0, so 3 and 2342 are divisors of 7026)
...
7026 / 82 = 85.682926829268 (the remainder is 56, so 82 is not a divisor of 7026)
7026 / 83 = 84.650602409639 (the remainder is 54, so 83 is not a divisor of 7026)