What are the divisors of 1485?

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

There is a total of 16 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 180.

16 odd divisors

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

How to compute the divisors of 1485?

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 1485 by each of the numbers from 1 to 1485 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)

1485 / 1 = 1485 (the remainder is 0, so 1 is a divisor of 1485)
1485 / 2 = 742.5 (the remainder is 1, so 2 is not a divisor of 1485)
1485 / 3 = 495 (the remainder is 0, so 3 is a divisor of 1485)
...
1485 / 1484 = 1.0006738544474 (the remainder is 1, so 1484 is not a divisor of 1485)
1485 / 1485 = 1 (the remainder is 0, so 1485 is a divisor of 1485)

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 1485 (i.e. 38.535697735995). 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 $\frac{N}{d} = D$ )

1485 / 1 = 1485 (the remainder is 0, so 1 and 1485 are divisors of 1485)
1485 / 2 = 742.5 (the remainder is 1, so 2 is not a divisor of 1485)
1485 / 3 = 495 (the remainder is 0, so 3 and 495 are divisors of 1485)
...
1485 / 37 = 40.135135135135 (the remainder is 5, so 37 is not a divisor of 1485)
1485 / 38 = 39.078947368421 (the remainder is 3, so 38 is not a divisor of 1485)