What are the divisors of 7066?

1, 2, 3533, 7066

There is a total of 4 positive divisors.
The sum of these divisors is 10602.
The arithmetic mean is 2650.5.

2 even divisors

2, 7066

2 odd divisors

1, 3533

How to compute the divisors of 7066?

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 7066 by each of the numbers from 1 to 7066 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)

7066 / 1 = 7066 (the remainder is 0, so 1 is a divisor of 7066)
7066 / 2 = 3533 (the remainder is 0, so 2 is a divisor of 7066)
7066 / 3 = 2355.3333333333 (the remainder is 1, so 3 is not a divisor of 7066)
...
7066 / 7065 = 1.0001415428167 (the remainder is 1, so 7065 is not a divisor of 7066)
7066 / 7066 = 1 (the remainder is 0, so 7066 is a divisor of 7066)

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 7066 (i.e. 84.05950273467). 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 $\frac{N}{d} = D$ )

7066 / 1 = 7066 (the remainder is 0, so 1 and 7066 are divisors of 7066)
7066 / 2 = 3533 (the remainder is 0, so 2 and 3533 are divisors of 7066)
7066 / 3 = 2355.3333333333 (the remainder is 1, so 3 is not a divisor of 7066)
...
7066 / 83 = 85.132530120482 (the remainder is 11, so 83 is not a divisor of 7066)
7066 / 84 = 84.119047619048 (the remainder is 10, so 84 is not a divisor of 7066)