What are the divisors of 4869?

1, 3, 9, 541, 1623, 4869

There is a total of 6 positive divisors.
The sum of these divisors is 7046.
The arithmetic mean is 1174.3333333333.

6 odd divisors

1, 3, 9, 541, 1623, 4869

How to compute the divisors of 4869?

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 4869 by each of the numbers from 1 to 4869 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)

4869 / 1 = 4869 (the remainder is 0, so 1 is a divisor of 4869)
4869 / 2 = 2434.5 (the remainder is 1, so 2 is not a divisor of 4869)
4869 / 3 = 1623 (the remainder is 0, so 3 is a divisor of 4869)
...
4869 / 4868 = 1.0002054231717 (the remainder is 1, so 4868 is not a divisor of 4869)
4869 / 4869 = 1 (the remainder is 0, so 4869 is a divisor of 4869)

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 4869 (i.e. 69.778220097678). 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 $\frac{N}{d} = D$ )

4869 / 1 = 4869 (the remainder is 0, so 1 and 4869 are divisors of 4869)
4869 / 2 = 2434.5 (the remainder is 1, so 2 is not a divisor of 4869)
4869 / 3 = 1623 (the remainder is 0, so 3 and 1623 are divisors of 4869)
...
4869 / 68 = 71.602941176471 (the remainder is 41, so 68 is not a divisor of 4869)
4869 / 69 = 70.565217391304 (the remainder is 39, so 69 is not a divisor of 4869)