What are the divisors of 4647?

1, 3, 1549, 4647

There is a total of 4 positive divisors.
The sum of these divisors is 6200.
The arithmetic mean is 1550.

4 odd divisors

1, 3, 1549, 4647

How to compute the divisors of 4647?

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 4647 by each of the numbers from 1 to 4647 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)

4647 / 1 = 4647 (the remainder is 0, so 1 is a divisor of 4647)
4647 / 2 = 2323.5 (the remainder is 1, so 2 is not a divisor of 4647)
4647 / 3 = 1549 (the remainder is 0, so 3 is a divisor of 4647)
...
4647 / 4646 = 1.0002152389152 (the remainder is 1, so 4646 is not a divisor of 4647)
4647 / 4647 = 1 (the remainder is 0, so 4647 is a divisor of 4647)

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 4647 (i.e. 68.168907868617). 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 $\frac{N}{d} = D$ )

4647 / 1 = 4647 (the remainder is 0, so 1 and 4647 are divisors of 4647)
4647 / 2 = 2323.5 (the remainder is 1, so 2 is not a divisor of 4647)
4647 / 3 = 1549 (the remainder is 0, so 3 and 1549 are divisors of 4647)
...
4647 / 67 = 69.358208955224 (the remainder is 24, so 67 is not a divisor of 4647)
4647 / 68 = 68.338235294118 (the remainder is 23, so 68 is not a divisor of 4647)