What are the divisors of 4868?

1, 2, 4, 1217, 2434, 4868

There is a total of 6 positive divisors.
The sum of these divisors is 8526.
The arithmetic mean is 1421.

4 even divisors

2, 4, 2434, 4868

2 odd divisors

1, 1217

How to compute the divisors of 4868?

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 4868 by each of the numbers from 1 to 4868 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)

4868 / 1 = 4868 (the remainder is 0, so 1 is a divisor of 4868)
4868 / 2 = 2434 (the remainder is 0, so 2 is a divisor of 4868)
4868 / 3 = 1622.6666666667 (the remainder is 2, so 3 is not a divisor of 4868)
...
4868 / 4867 = 1.0002054653791 (the remainder is 1, so 4867 is not a divisor of 4868)
4868 / 4868 = 1 (the remainder is 0, so 4868 is a divisor of 4868)

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 4868 (i.e. 69.77105417005). 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 $\frac{N}{d} = D$ )

4868 / 1 = 4868 (the remainder is 0, so 1 and 4868 are divisors of 4868)
4868 / 2 = 2434 (the remainder is 0, so 2 and 2434 are divisors of 4868)
4868 / 3 = 1622.6666666667 (the remainder is 2, so 3 is not a divisor of 4868)
...
4868 / 68 = 71.588235294118 (the remainder is 40, so 68 is not a divisor of 4868)
4868 / 69 = 70.550724637681 (the remainder is 38, so 69 is not a divisor of 4868)