What are the divisors of 4834?

1, 2, 2417, 4834

There is a total of 4 positive divisors.
The sum of these divisors is 7254.
The arithmetic mean is 1813.5.

2 even divisors

2, 4834

2 odd divisors

1, 2417

How to compute the divisors of 4834?

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 4834 by each of the numbers from 1 to 4834 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)

4834 / 1 = 4834 (the remainder is 0, so 1 is a divisor of 4834)
4834 / 2 = 2417 (the remainder is 0, so 2 is a divisor of 4834)
4834 / 3 = 1611.3333333333 (the remainder is 1, so 3 is not a divisor of 4834)
...
4834 / 4833 = 1.0002069108214 (the remainder is 1, so 4833 is not a divisor of 4834)
4834 / 4834 = 1 (the remainder is 0, so 4834 is a divisor of 4834)

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 4834 (i.e. 69.526973183075). 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 $\frac{N}{d} = D$ )

4834 / 1 = 4834 (the remainder is 0, so 1 and 4834 are divisors of 4834)
4834 / 2 = 2417 (the remainder is 0, so 2 and 2417 are divisors of 4834)
4834 / 3 = 1611.3333333333 (the remainder is 1, so 3 is not a divisor of 4834)
...
4834 / 68 = 71.088235294118 (the remainder is 6, so 68 is not a divisor of 4834)
4834 / 69 = 70.057971014493 (the remainder is 4, so 69 is not a divisor of 4834)