What are the divisors of 4545?

1, 3, 5, 9, 15, 45, 101, 303, 505, 909, 1515, 4545

There is a total of 12 positive divisors.
The sum of these divisors is 7956.
The arithmetic mean is 663.

12 odd divisors

1, 3, 5, 9, 15, 45, 101, 303, 505, 909, 1515, 4545

How to compute the divisors of 4545?

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 4545 by each of the numbers from 1 to 4545 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)

4545 / 1 = 4545 (the remainder is 0, so 1 is a divisor of 4545)
4545 / 2 = 2272.5 (the remainder is 1, so 2 is not a divisor of 4545)
4545 / 3 = 1515 (the remainder is 0, so 3 is a divisor of 4545)
...
4545 / 4544 = 1.0002200704225 (the remainder is 1, so 4544 is not a divisor of 4545)
4545 / 4545 = 1 (the remainder is 0, so 4545 is a divisor of 4545)

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 4545 (i.e. 67.416615162733). 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 $\frac{N}{d} = D$ )

4545 / 1 = 4545 (the remainder is 0, so 1 and 4545 are divisors of 4545)
4545 / 2 = 2272.5 (the remainder is 1, so 2 is not a divisor of 4545)
4545 / 3 = 1515 (the remainder is 0, so 3 and 1515 are divisors of 4545)
...
4545 / 66 = 68.863636363636 (the remainder is 57, so 66 is not a divisor of 4545)
4545 / 67 = 67.835820895522 (the remainder is 56, so 67 is not a divisor of 4545)