What are the divisors of 4623?

1, 3, 23, 67, 69, 201, 1541, 4623

There is a total of 8 positive divisors.
The sum of these divisors is 6528.
The arithmetic mean is 816.

8 odd divisors

1, 3, 23, 67, 69, 201, 1541, 4623

How to compute the divisors of 4623?

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 4623 by each of the numbers from 1 to 4623 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)

4623 / 1 = 4623 (the remainder is 0, so 1 is a divisor of 4623)
4623 / 2 = 2311.5 (the remainder is 1, so 2 is not a divisor of 4623)
4623 / 3 = 1541 (the remainder is 0, so 3 is a divisor of 4623)
...
4623 / 4622 = 1.0002163565556 (the remainder is 1, so 4622 is not a divisor of 4623)
4623 / 4623 = 1 (the remainder is 0, so 4623 is a divisor of 4623)

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 4623 (i.e. 67.992646661238). 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 $\frac{N}{d} = D$ )

4623 / 1 = 4623 (the remainder is 0, so 1 and 4623 are divisors of 4623)
4623 / 2 = 2311.5 (the remainder is 1, so 2 is not a divisor of 4623)
4623 / 3 = 1541 (the remainder is 0, so 3 and 1541 are divisors of 4623)
...
4623 / 66 = 70.045454545455 (the remainder is 3, so 66 is not a divisor of 4623)
4623 / 67 = 69 (the remainder is 0, so 67 and 69 are divisors of 4623)