What are the divisors of 1449?

1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483, 1449

There is a total of 12 positive divisors.
The sum of these divisors is 2496.
The arithmetic mean is 208.

12 odd divisors

1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483, 1449

How to compute the divisors of 1449?

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 1449 by each of the numbers from 1 to 1449 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)

1449 / 1 = 1449 (the remainder is 0, so 1 is a divisor of 1449)
1449 / 2 = 724.5 (the remainder is 1, so 2 is not a divisor of 1449)
1449 / 3 = 483 (the remainder is 0, so 3 is a divisor of 1449)
...
1449 / 1448 = 1.0006906077348 (the remainder is 1, so 1448 is not a divisor of 1449)
1449 / 1449 = 1 (the remainder is 0, so 1449 is a divisor of 1449)

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 1449 (i.e. 38.065732621349). 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 $\frac{N}{d} = D$ )

1449 / 1 = 1449 (the remainder is 0, so 1 and 1449 are divisors of 1449)
1449 / 2 = 724.5 (the remainder is 1, so 2 is not a divisor of 1449)
1449 / 3 = 483 (the remainder is 0, so 3 and 483 are divisors of 1449)
...
1449 / 37 = 39.162162162162 (the remainder is 6, so 37 is not a divisor of 1449)
1449 / 38 = 38.131578947368 (the remainder is 5, so 38 is not a divisor of 1449)