What are the divisors of 8014?

1, 2, 4007, 8014

There is a total of 4 positive divisors.
The sum of these divisors is 12024.
The arithmetic mean is 3006.

2 even divisors

2, 8014

2 odd divisors

1, 4007

How to compute the divisors of 8014?

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 8014 by each of the numbers from 1 to 8014 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)

8014 / 1 = 8014 (the remainder is 0, so 1 is a divisor of 8014)
8014 / 2 = 4007 (the remainder is 0, so 2 is a divisor of 8014)
8014 / 3 = 2671.3333333333 (the remainder is 1, so 3 is not a divisor of 8014)
...
8014 / 8013 = 1.0001247972045 (the remainder is 1, so 8013 is not a divisor of 8014)
8014 / 8014 = 1 (the remainder is 0, so 8014 is a divisor of 8014)

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 8014 (i.e. 89.52094726934). 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 $\frac{N}{d} = D$ )

8014 / 1 = 8014 (the remainder is 0, so 1 and 8014 are divisors of 8014)
8014 / 2 = 4007 (the remainder is 0, so 2 and 4007 are divisors of 8014)
8014 / 3 = 2671.3333333333 (the remainder is 1, so 3 is not a divisor of 8014)
...
8014 / 88 = 91.068181818182 (the remainder is 6, so 88 is not a divisor of 8014)
8014 / 89 = 90.044943820225 (the remainder is 4, so 89 is not a divisor of 8014)