What are the divisors of 4841?

1, 47, 103, 4841

There is a total of 4 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 1248.

4 odd divisors

1, 47, 103, 4841

How to compute the divisors of 4841?

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 4841 by each of the numbers from 1 to 4841 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)

4841 / 1 = 4841 (the remainder is 0, so 1 is a divisor of 4841)
4841 / 2 = 2420.5 (the remainder is 1, so 2 is not a divisor of 4841)
4841 / 3 = 1613.6666666667 (the remainder is 2, so 3 is not a divisor of 4841)
...
4841 / 4840 = 1.0002066115702 (the remainder is 1, so 4840 is not a divisor of 4841)
4841 / 4841 = 1 (the remainder is 0, so 4841 is a divisor of 4841)

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 4841 (i.e. 69.577295147196). 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 $\frac{N}{d} = D$ )

4841 / 1 = 4841 (the remainder is 0, so 1 and 4841 are divisors of 4841)
4841 / 2 = 2420.5 (the remainder is 1, so 2 is not a divisor of 4841)
4841 / 3 = 1613.6666666667 (the remainder is 2, so 3 is not a divisor of 4841)
...
4841 / 68 = 71.191176470588 (the remainder is 13, so 68 is not a divisor of 4841)
4841 / 69 = 70.159420289855 (the remainder is 11, so 69 is not a divisor of 4841)