What are the divisors of 4554?

1, 2, 3, 6, 9, 11, 18, 22, 23, 33, 46, 66, 69, 99, 138, 198, 207, 253, 414, 506, 759, 1518, 2277, 4554

There is a total of 24 positive divisors.
The sum of these divisors is 11232.
The arithmetic mean is 468.

12 even divisors

2, 6, 18, 22, 46, 66, 138, 198, 414, 506, 1518, 4554

12 odd divisors

1, 3, 9, 11, 23, 33, 69, 99, 207, 253, 759, 2277

How to compute the divisors of 4554?

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 4554 by each of the numbers from 1 to 4554 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)

4554 / 1 = 4554 (the remainder is 0, so 1 is a divisor of 4554)
4554 / 2 = 2277 (the remainder is 0, so 2 is a divisor of 4554)
4554 / 3 = 1518 (the remainder is 0, so 3 is a divisor of 4554)
...
4554 / 4553 = 1.0002196354052 (the remainder is 1, so 4553 is not a divisor of 4554)
4554 / 4554 = 1 (the remainder is 0, so 4554 is a divisor of 4554)

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 4554 (i.e. 67.483331275212). 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 $\frac{N}{d} = D$ )

4554 / 1 = 4554 (the remainder is 0, so 1 and 4554 are divisors of 4554)
4554 / 2 = 2277 (the remainder is 0, so 2 and 2277 are divisors of 4554)
4554 / 3 = 1518 (the remainder is 0, so 3 and 1518 are divisors of 4554)
...
4554 / 66 = 69 (the remainder is 0, so 66 and 69 are divisors of 4554)
4554 / 67 = 67.970149253731 (the remainder is 65, so 67 is not a divisor of 4554)