What are the divisors of 4838?

1, 2, 41, 59, 82, 118, 2419, 4838

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

4 even divisors

2, 82, 118, 4838

4 odd divisors

1, 41, 59, 2419

How to compute the divisors of 4838?

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 4838 by each of the numbers from 1 to 4838 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)

4838 / 1 = 4838 (the remainder is 0, so 1 is a divisor of 4838)
4838 / 2 = 2419 (the remainder is 0, so 2 is a divisor of 4838)
4838 / 3 = 1612.6666666667 (the remainder is 2, so 3 is not a divisor of 4838)
...
4838 / 4837 = 1.0002067397147 (the remainder is 1, so 4837 is not a divisor of 4838)
4838 / 4838 = 1 (the remainder is 0, so 4838 is a divisor of 4838)

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 4838 (i.e. 69.555733049117). 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 $\frac{N}{d} = D$ )

4838 / 1 = 4838 (the remainder is 0, so 1 and 4838 are divisors of 4838)
4838 / 2 = 2419 (the remainder is 0, so 2 and 2419 are divisors of 4838)
4838 / 3 = 1612.6666666667 (the remainder is 2, so 3 is not a divisor of 4838)
...
4838 / 68 = 71.147058823529 (the remainder is 10, so 68 is not a divisor of 4838)
4838 / 69 = 70.115942028986 (the remainder is 8, so 69 is not a divisor of 4838)