What are the divisors of 4455?

1, 3, 5, 9, 11, 15, 27, 33, 45, 55, 81, 99, 135, 165, 297, 405, 495, 891, 1485, 4455

There is a total of 20 positive divisors.
The sum of these divisors is 8712.
The arithmetic mean is 435.6.

20 odd divisors

1, 3, 5, 9, 11, 15, 27, 33, 45, 55, 81, 99, 135, 165, 297, 405, 495, 891, 1485, 4455

How to compute the divisors of 4455?

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 4455 by each of the numbers from 1 to 4455 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)

4455 / 1 = 4455 (the remainder is 0, so 1 is a divisor of 4455)
4455 / 2 = 2227.5 (the remainder is 1, so 2 is not a divisor of 4455)
4455 / 3 = 1485 (the remainder is 0, so 3 is a divisor of 4455)
...
4455 / 4454 = 1.0002245172878 (the remainder is 1, so 4454 is not a divisor of 4455)
4455 / 4455 = 1 (the remainder is 0, so 4455 is a divisor of 4455)

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 4455 (i.e. 66.745786383861). 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 $\frac{N}{d} = D$ )

4455 / 1 = 4455 (the remainder is 0, so 1 and 4455 are divisors of 4455)
4455 / 2 = 2227.5 (the remainder is 1, so 2 is not a divisor of 4455)
4455 / 3 = 1485 (the remainder is 0, so 3 and 1485 are divisors of 4455)
...
4455 / 65 = 68.538461538462 (the remainder is 35, so 65 is not a divisor of 4455)
4455 / 66 = 67.5 (the remainder is 33, so 66 is not a divisor of 4455)