What are the divisors of 4874?

1, 2, 2437, 4874

There is a total of 4 positive divisors.
The sum of these divisors is 7314.
The arithmetic mean is 1828.5.

2 even divisors

2, 4874

2 odd divisors

1, 2437

How to compute the divisors of 4874?

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 4874 by each of the numbers from 1 to 4874 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)

4874 / 1 = 4874 (the remainder is 0, so 1 is a divisor of 4874)
4874 / 2 = 2437 (the remainder is 0, so 2 is a divisor of 4874)
4874 / 3 = 1624.6666666667 (the remainder is 2, so 3 is not a divisor of 4874)
...
4874 / 4873 = 1.0002052123948 (the remainder is 1, so 4873 is not a divisor of 4874)
4874 / 4874 = 1 (the remainder is 0, so 4874 is a divisor of 4874)

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 4874 (i.e. 69.814038702828). 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 $\frac{N}{d} = D$ )

4874 / 1 = 4874 (the remainder is 0, so 1 and 4874 are divisors of 4874)
4874 / 2 = 2437 (the remainder is 0, so 2 and 2437 are divisors of 4874)
4874 / 3 = 1624.6666666667 (the remainder is 2, so 3 is not a divisor of 4874)
...
4874 / 68 = 71.676470588235 (the remainder is 46, so 68 is not a divisor of 4874)
4874 / 69 = 70.63768115942 (the remainder is 44, so 69 is not a divisor of 4874)