What are the divisors of 7069?

1, 7069

There is a total of 2 positive divisors.
The sum of these divisors is 7070.
The arithmetic mean is 3535.

2 odd divisors

1, 7069

How to compute the divisors of 7069?

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 7069 by each of the numbers from 1 to 7069 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)

7069 / 1 = 7069 (the remainder is 0, so 1 is a divisor of 7069)
7069 / 2 = 3534.5 (the remainder is 1, so 2 is not a divisor of 7069)
7069 / 3 = 2356.3333333333 (the remainder is 1, so 3 is not a divisor of 7069)
...
7069 / 7068 = 1.0001414827391 (the remainder is 1, so 7068 is not a divisor of 7069)
7069 / 7069 = 1 (the remainder is 0, so 7069 is a divisor of 7069)

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 7069 (i.e. 84.07734534344). 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 $\frac{N}{d} = D$ )

7069 / 1 = 7069 (the remainder is 0, so 1 and 7069 are divisors of 7069)
7069 / 2 = 3534.5 (the remainder is 1, so 2 is not a divisor of 7069)
7069 / 3 = 2356.3333333333 (the remainder is 1, so 3 is not a divisor of 7069)
...
7069 / 83 = 85.168674698795 (the remainder is 14, so 83 is not a divisor of 7069)
7069 / 84 = 84.154761904762 (the remainder is 13, so 84 is not a divisor of 7069)