What are the divisors of 7064?

1, 2, 4, 8, 883, 1766, 3532, 7064

There is a total of 8 positive divisors.
The sum of these divisors is 13260.
The arithmetic mean is 1657.5.

6 even divisors

2, 4, 8, 1766, 3532, 7064

2 odd divisors

1, 883

How to compute the divisors of 7064?

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 7064 by each of the numbers from 1 to 7064 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)

7064 / 1 = 7064 (the remainder is 0, so 1 is a divisor of 7064)
7064 / 2 = 3532 (the remainder is 0, so 2 is a divisor of 7064)
7064 / 3 = 2354.6666666667 (the remainder is 2, so 3 is not a divisor of 7064)
...
7064 / 7063 = 1.0001415828968 (the remainder is 1, so 7063 is not a divisor of 7064)
7064 / 7064 = 1 (the remainder is 0, so 7064 is a divisor of 7064)

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 7064 (i.e. 84.047605557803). 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 $\frac{N}{d} = D$ )

7064 / 1 = 7064 (the remainder is 0, so 1 and 7064 are divisors of 7064)
7064 / 2 = 3532 (the remainder is 0, so 2 and 3532 are divisors of 7064)
7064 / 3 = 2354.6666666667 (the remainder is 2, so 3 is not a divisor of 7064)
...
7064 / 83 = 85.10843373494 (the remainder is 9, so 83 is not a divisor of 7064)
7064 / 84 = 84.095238095238 (the remainder is 8, so 84 is not a divisor of 7064)