What are the divisors of 8048?

1, 2, 4, 8, 16, 503, 1006, 2012, 4024, 8048

There is a total of 10 positive divisors.
The sum of these divisors is 15624.
The arithmetic mean is 1562.4.

8 even divisors

2, 4, 8, 16, 1006, 2012, 4024, 8048

2 odd divisors

1, 503

How to compute the divisors of 8048?

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 8048 by each of the numbers from 1 to 8048 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)

8048 / 1 = 8048 (the remainder is 0, so 1 is a divisor of 8048)
8048 / 2 = 4024 (the remainder is 0, so 2 is a divisor of 8048)
8048 / 3 = 2682.6666666667 (the remainder is 2, so 3 is not a divisor of 8048)
...
8048 / 8047 = 1.0001242699143 (the remainder is 1, so 8047 is not a divisor of 8048)
8048 / 8048 = 1 (the remainder is 0, so 8048 is a divisor of 8048)

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 8048 (i.e. 89.710645968023). 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 $\frac{N}{d} = D$ )

8048 / 1 = 8048 (the remainder is 0, so 1 and 8048 are divisors of 8048)
8048 / 2 = 4024 (the remainder is 0, so 2 and 4024 are divisors of 8048)
8048 / 3 = 2682.6666666667 (the remainder is 2, so 3 is not a divisor of 8048)
...
8048 / 88 = 91.454545454545 (the remainder is 40, so 88 is not a divisor of 8048)
8048 / 89 = 90.426966292135 (the remainder is 38, so 89 is not a divisor of 8048)