What are the divisors of 4541?

1, 19, 239, 4541

There is a total of 4 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 1200.

4 odd divisors

1, 19, 239, 4541

How to compute the divisors of 4541?

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 4541 by each of the numbers from 1 to 4541 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)

4541 / 1 = 4541 (the remainder is 0, so 1 is a divisor of 4541)
4541 / 2 = 2270.5 (the remainder is 1, so 2 is not a divisor of 4541)
4541 / 3 = 1513.6666666667 (the remainder is 2, so 3 is not a divisor of 4541)
...
4541 / 4540 = 1.0002202643172 (the remainder is 1, so 4540 is not a divisor of 4541)
4541 / 4541 = 1 (the remainder is 0, so 4541 is a divisor of 4541)

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 4541 (i.e. 67.386942355326). 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 $\frac{N}{d} = D$ )

4541 / 1 = 4541 (the remainder is 0, so 1 and 4541 are divisors of 4541)
4541 / 2 = 2270.5 (the remainder is 1, so 2 is not a divisor of 4541)
4541 / 3 = 1513.6666666667 (the remainder is 2, so 3 is not a divisor of 4541)
...
4541 / 66 = 68.80303030303 (the remainder is 53, so 66 is not a divisor of 4541)
4541 / 67 = 67.776119402985 (the remainder is 52, so 67 is not a divisor of 4541)