What are the divisors of 5048?

1, 2, 4, 8, 631, 1262, 2524, 5048

There is a total of 8 positive divisors.
The sum of these divisors is 9480.
The arithmetic mean is 1185.

6 even divisors

2, 4, 8, 1262, 2524, 5048

2 odd divisors

1, 631

How to compute the divisors of 5048?

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 5048 by each of the numbers from 1 to 5048 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)

5048 / 1 = 5048 (the remainder is 0, so 1 is a divisor of 5048)
5048 / 2 = 2524 (the remainder is 0, so 2 is a divisor of 5048)
5048 / 3 = 1682.6666666667 (the remainder is 2, so 3 is not a divisor of 5048)
...
5048 / 5047 = 1.0001981375074 (the remainder is 1, so 5047 is not a divisor of 5048)
5048 / 5048 = 1 (the remainder is 0, so 5048 is a divisor of 5048)

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 5048 (i.e. 71.049278673326). 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 $\frac{N}{d} = D$ )

5048 / 1 = 5048 (the remainder is 0, so 1 and 5048 are divisors of 5048)
5048 / 2 = 2524 (the remainder is 0, so 2 and 2524 are divisors of 5048)
5048 / 3 = 1682.6666666667 (the remainder is 2, so 3 is not a divisor of 5048)
...
5048 / 70 = 72.114285714286 (the remainder is 8, so 70 is not a divisor of 5048)
5048 / 71 = 71.098591549296 (the remainder is 7, so 71 is not a divisor of 5048)