What are the divisors of 1467?

1, 3, 9, 163, 489, 1467

There is a total of 6 positive divisors.
The sum of these divisors is 2132.
The arithmetic mean is 355.33333333333.

6 odd divisors

1, 3, 9, 163, 489, 1467

How to compute the divisors of 1467?

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 1467 by each of the numbers from 1 to 1467 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)

1467 / 1 = 1467 (the remainder is 0, so 1 is a divisor of 1467)
1467 / 2 = 733.5 (the remainder is 1, so 2 is not a divisor of 1467)
1467 / 3 = 489 (the remainder is 0, so 3 is a divisor of 1467)
...
1467 / 1466 = 1.0006821282401 (the remainder is 1, so 1466 is not a divisor of 1467)
1467 / 1467 = 1 (the remainder is 0, so 1467 is a divisor of 1467)

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 1467 (i.e. 38.301436004411). 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 $\frac{N}{d} = D$ )

1467 / 1 = 1467 (the remainder is 0, so 1 and 1467 are divisors of 1467)
1467 / 2 = 733.5 (the remainder is 1, so 2 is not a divisor of 1467)
1467 / 3 = 489 (the remainder is 0, so 3 and 489 are divisors of 1467)
...
1467 / 37 = 39.648648648649 (the remainder is 24, so 37 is not a divisor of 1467)
1467 / 38 = 38.605263157895 (the remainder is 23, so 38 is not a divisor of 1467)