What are the divisors of 4882?

1, 2, 2441, 4882

There is a total of 4 positive divisors.
The sum of these divisors is 7326.
The arithmetic mean is 1831.5.

2 even divisors

2, 4882

2 odd divisors

1, 2441

How to compute the divisors of 4882?

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 4882 by each of the numbers from 1 to 4882 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)

4882 / 1 = 4882 (the remainder is 0, so 1 is a divisor of 4882)
4882 / 2 = 2441 (the remainder is 0, so 2 is a divisor of 4882)
4882 / 3 = 1627.3333333333 (the remainder is 1, so 3 is not a divisor of 4882)
...
4882 / 4881 = 1.00020487605 (the remainder is 1, so 4881 is not a divisor of 4882)
4882 / 4882 = 1 (the remainder is 0, so 4882 is a divisor of 4882)

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 4882 (i.e. 69.871310278254). 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 $\frac{N}{d} = D$ )

4882 / 1 = 4882 (the remainder is 0, so 1 and 4882 are divisors of 4882)
4882 / 2 = 2441 (the remainder is 0, so 2 and 2441 are divisors of 4882)
4882 / 3 = 1627.3333333333 (the remainder is 1, so 3 is not a divisor of 4882)
...
4882 / 68 = 71.794117647059 (the remainder is 54, so 68 is not a divisor of 4882)
4882 / 69 = 70.753623188406 (the remainder is 52, so 69 is not a divisor of 4882)