What are the divisors of 4808?

1, 2, 4, 8, 601, 1202, 2404, 4808

There is a total of 8 positive divisors.
The sum of these divisors is 9030.
The arithmetic mean is 1128.75.

6 even divisors

2, 4, 8, 1202, 2404, 4808

2 odd divisors

1, 601

How to compute the divisors of 4808?

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 4808 by each of the numbers from 1 to 4808 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)

4808 / 1 = 4808 (the remainder is 0, so 1 is a divisor of 4808)
4808 / 2 = 2404 (the remainder is 0, so 2 is a divisor of 4808)
4808 / 3 = 1602.6666666667 (the remainder is 2, so 3 is not a divisor of 4808)
...
4808 / 4807 = 1.0002080299563 (the remainder is 1, so 4807 is not a divisor of 4808)
4808 / 4808 = 1 (the remainder is 0, so 4808 is a divisor of 4808)

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 4808 (i.e. 69.339743293439). 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 $\frac{N}{d} = D$ )

4808 / 1 = 4808 (the remainder is 0, so 1 and 4808 are divisors of 4808)
4808 / 2 = 2404 (the remainder is 0, so 2 and 2404 are divisors of 4808)
4808 / 3 = 1602.6666666667 (the remainder is 2, so 3 is not a divisor of 4808)
...
4808 / 68 = 70.705882352941 (the remainder is 48, so 68 is not a divisor of 4808)
4808 / 69 = 69.68115942029 (the remainder is 47, so 69 is not a divisor of 4808)