What are the divisors of 8026?

1, 2, 4013, 8026

There is a total of 4 positive divisors.
The sum of these divisors is 12042.
The arithmetic mean is 3010.5.

2 even divisors

2, 8026

2 odd divisors

1, 4013

How to compute the divisors of 8026?

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 8026 by each of the numbers from 1 to 8026 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)

8026 / 1 = 8026 (the remainder is 0, so 1 is a divisor of 8026)
8026 / 2 = 4013 (the remainder is 0, so 2 is a divisor of 8026)
8026 / 3 = 2675.3333333333 (the remainder is 1, so 3 is not a divisor of 8026)
...
8026 / 8025 = 1.0001246105919 (the remainder is 1, so 8025 is not a divisor of 8026)
8026 / 8026 = 1 (the remainder is 0, so 8026 is a divisor of 8026)

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 8026 (i.e. 89.5879456177). 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 $\frac{N}{d} = D$ )

8026 / 1 = 8026 (the remainder is 0, so 1 and 8026 are divisors of 8026)
8026 / 2 = 4013 (the remainder is 0, so 2 and 4013 are divisors of 8026)
8026 / 3 = 2675.3333333333 (the remainder is 1, so 3 is not a divisor of 8026)
...
8026 / 88 = 91.204545454545 (the remainder is 18, so 88 is not a divisor of 8026)
8026 / 89 = 90.179775280899 (the remainder is 16, so 89 is not a divisor of 8026)