What are the divisors of 7047?

1, 3, 9, 27, 29, 81, 87, 243, 261, 783, 2349, 7047

There is a total of 12 positive divisors.
The sum of these divisors is 10920.
The arithmetic mean is 910.

12 odd divisors

1, 3, 9, 27, 29, 81, 87, 243, 261, 783, 2349, 7047

How to compute the divisors of 7047?

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 7047 by each of the numbers from 1 to 7047 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)

7047 / 1 = 7047 (the remainder is 0, so 1 is a divisor of 7047)
7047 / 2 = 3523.5 (the remainder is 1, so 2 is not a divisor of 7047)
7047 / 3 = 2349 (the remainder is 0, so 3 is a divisor of 7047)
...
7047 / 7046 = 1.0001419244962 (the remainder is 1, so 7046 is not a divisor of 7047)
7047 / 7047 = 1 (the remainder is 0, so 7047 is a divisor of 7047)

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 7047 (i.e. 83.946411477799). 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 $\frac{N}{d} = D$ )

7047 / 1 = 7047 (the remainder is 0, so 1 and 7047 are divisors of 7047)
7047 / 2 = 3523.5 (the remainder is 1, so 2 is not a divisor of 7047)
7047 / 3 = 2349 (the remainder is 0, so 3 and 2349 are divisors of 7047)
...
7047 / 82 = 85.939024390244 (the remainder is 77, so 82 is not a divisor of 7047)
7047 / 83 = 84.903614457831 (the remainder is 75, so 83 is not a divisor of 7047)