What are the divisors of 4798?

1, 2, 2399, 4798

There is a total of 4 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 1800.

2 even divisors

2, 4798

2 odd divisors

1, 2399

How to compute the divisors of 4798?

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 4798 by each of the numbers from 1 to 4798 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)

4798 / 1 = 4798 (the remainder is 0, so 1 is a divisor of 4798)
4798 / 2 = 2399 (the remainder is 0, so 2 is a divisor of 4798)
4798 / 3 = 1599.3333333333 (the remainder is 1, so 3 is not a divisor of 4798)
...
4798 / 4797 = 1.0002084636231 (the remainder is 1, so 4797 is not a divisor of 4798)
4798 / 4798 = 1 (the remainder is 0, so 4798 is a divisor of 4798)

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 4798 (i.e. 69.267597042196). 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 $\frac{N}{d} = D$ )

4798 / 1 = 4798 (the remainder is 0, so 1 and 4798 are divisors of 4798)
4798 / 2 = 2399 (the remainder is 0, so 2 and 2399 are divisors of 4798)
4798 / 3 = 1599.3333333333 (the remainder is 1, so 3 is not a divisor of 4798)
...
4798 / 68 = 70.558823529412 (the remainder is 38, so 68 is not a divisor of 4798)
4798 / 69 = 69.536231884058 (the remainder is 37, so 69 is not a divisor of 4798)