What are the divisors of 4876?

1, 2, 4, 23, 46, 53, 92, 106, 212, 1219, 2438, 4876

There is a total of 12 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 756.

8 even divisors

2, 4, 46, 92, 106, 212, 2438, 4876

4 odd divisors

1, 23, 53, 1219

How to compute the divisors of 4876?

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 4876 by each of the numbers from 1 to 4876 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)

4876 / 1 = 4876 (the remainder is 0, so 1 is a divisor of 4876)
4876 / 2 = 2438 (the remainder is 0, so 2 is a divisor of 4876)
4876 / 3 = 1625.3333333333 (the remainder is 1, so 3 is not a divisor of 4876)
...
4876 / 4875 = 1.0002051282051 (the remainder is 1, so 4875 is not a divisor of 4876)
4876 / 4876 = 1 (the remainder is 0, so 4876 is a divisor of 4876)

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 4876 (i.e. 69.828361000384). 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 $\frac{N}{d} = D$ )

4876 / 1 = 4876 (the remainder is 0, so 1 and 4876 are divisors of 4876)
4876 / 2 = 2438 (the remainder is 0, so 2 and 2438 are divisors of 4876)
4876 / 3 = 1625.3333333333 (the remainder is 1, so 3 is not a divisor of 4876)
...
4876 / 68 = 71.705882352941 (the remainder is 48, so 68 is not a divisor of 4876)
4876 / 69 = 70.666666666667 (the remainder is 46, so 69 is not a divisor of 4876)