What are the divisors of 4547?

1, 4547

There is a total of 2 positive divisors.
The sum of these divisors is 4548.
The arithmetic mean is 2274.

2 odd divisors

1, 4547

How to compute the divisors of 4547?

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 4547 by each of the numbers from 1 to 4547 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)

4547 / 1 = 4547 (the remainder is 0, so 1 is a divisor of 4547)
4547 / 2 = 2273.5 (the remainder is 1, so 2 is not a divisor of 4547)
4547 / 3 = 1515.6666666667 (the remainder is 2, so 3 is not a divisor of 4547)
...
4547 / 4546 = 1.0002199736032 (the remainder is 1, so 4546 is not a divisor of 4547)
4547 / 4547 = 1 (the remainder is 0, so 4547 is a divisor of 4547)

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 4547 (i.e. 67.431446669933). 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 $\frac{N}{d} = D$ )

4547 / 1 = 4547 (the remainder is 0, so 1 and 4547 are divisors of 4547)
4547 / 2 = 2273.5 (the remainder is 1, so 2 is not a divisor of 4547)
4547 / 3 = 1515.6666666667 (the remainder is 2, so 3 is not a divisor of 4547)
...
4547 / 66 = 68.893939393939 (the remainder is 59, so 66 is not a divisor of 4547)
4547 / 67 = 67.865671641791 (the remainder is 58, so 67 is not a divisor of 4547)