What are the divisors of 4822?

1, 2, 2411, 4822

There is a total of 4 positive divisors.
The sum of these divisors is 7236.
The arithmetic mean is 1809.

2 even divisors

2, 4822

2 odd divisors

1, 2411

How to compute the divisors of 4822?

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 4822 by each of the numbers from 1 to 4822 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)

4822 / 1 = 4822 (the remainder is 0, so 1 is a divisor of 4822)
4822 / 2 = 2411 (the remainder is 0, so 2 is a divisor of 4822)
4822 / 3 = 1607.3333333333 (the remainder is 1, so 3 is not a divisor of 4822)
...
4822 / 4821 = 1.0002074258453 (the remainder is 1, so 4821 is not a divisor of 4822)
4822 / 4822 = 1 (the remainder is 0, so 4822 is a divisor of 4822)

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 4822 (i.e. 69.440622117029). 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 $\frac{N}{d} = D$ )

4822 / 1 = 4822 (the remainder is 0, so 1 and 4822 are divisors of 4822)
4822 / 2 = 2411 (the remainder is 0, so 2 and 2411 are divisors of 4822)
4822 / 3 = 1607.3333333333 (the remainder is 1, so 3 is not a divisor of 4822)
...
4822 / 68 = 70.911764705882 (the remainder is 62, so 68 is not a divisor of 4822)
4822 / 69 = 69.884057971014 (the remainder is 61, so 69 is not a divisor of 4822)