What are the divisors of 4827?

1, 3, 1609, 4827

There is a total of 4 positive divisors.
The sum of these divisors is 6440.
The arithmetic mean is 1610.

4 odd divisors

1, 3, 1609, 4827

How to compute the divisors of 4827?

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 4827 by each of the numbers from 1 to 4827 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)

4827 / 1 = 4827 (the remainder is 0, so 1 is a divisor of 4827)
4827 / 2 = 2413.5 (the remainder is 1, so 2 is not a divisor of 4827)
4827 / 3 = 1609 (the remainder is 0, so 3 is a divisor of 4827)
...
4827 / 4826 = 1.0002072109407 (the remainder is 1, so 4826 is not a divisor of 4827)
4827 / 4827 = 1 (the remainder is 0, so 4827 is a divisor of 4827)

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 4827 (i.e. 69.476614770727). 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 $\frac{N}{d} = D$ )

4827 / 1 = 4827 (the remainder is 0, so 1 and 4827 are divisors of 4827)
4827 / 2 = 2413.5 (the remainder is 1, so 2 is not a divisor of 4827)
4827 / 3 = 1609 (the remainder is 0, so 3 and 1609 are divisors of 4827)
...
4827 / 68 = 70.985294117647 (the remainder is 67, so 68 is not a divisor of 4827)
4827 / 69 = 69.95652173913 (the remainder is 66, so 69 is not a divisor of 4827)