What are the divisors of 1458?

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458

There is a total of 14 positive divisors.
The sum of these divisors is 3279.
The arithmetic mean is 234.21428571429.

7 even divisors

2, 6, 18, 54, 162, 486, 1458

7 odd divisors

1, 3, 9, 27, 81, 243, 729

How to compute the divisors of 1458?

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 1458 by each of the numbers from 1 to 1458 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)

1458 / 1 = 1458 (the remainder is 0, so 1 is a divisor of 1458)
1458 / 2 = 729 (the remainder is 0, so 2 is a divisor of 1458)
1458 / 3 = 486 (the remainder is 0, so 3 is a divisor of 1458)
...
1458 / 1457 = 1.0006863417982 (the remainder is 1, so 1457 is not a divisor of 1458)
1458 / 1458 = 1 (the remainder is 0, so 1458 is a divisor of 1458)

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 1458 (i.e. 38.183766184074). 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 $\frac{N}{d} = D$ )

1458 / 1 = 1458 (the remainder is 0, so 1 and 1458 are divisors of 1458)
1458 / 2 = 729 (the remainder is 0, so 2 and 729 are divisors of 1458)
1458 / 3 = 486 (the remainder is 0, so 3 and 486 are divisors of 1458)
...
1458 / 37 = 39.405405405405 (the remainder is 15, so 37 is not a divisor of 1458)
1458 / 38 = 38.368421052632 (the remainder is 14, so 38 is not a divisor of 1458)