What are the divisors of 1452?

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 121, 132, 242, 363, 484, 726, 1452

There is a total of 18 positive divisors.
The sum of these divisors is 3724.
The arithmetic mean is 206.88888888889.

12 even divisors

2, 4, 6, 12, 22, 44, 66, 132, 242, 484, 726, 1452

6 odd divisors

1, 3, 11, 33, 121, 363

How to compute the divisors of 1452?

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 1452 by each of the numbers from 1 to 1452 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)

1452 / 1 = 1452 (the remainder is 0, so 1 is a divisor of 1452)
1452 / 2 = 726 (the remainder is 0, so 2 is a divisor of 1452)
1452 / 3 = 484 (the remainder is 0, so 3 is a divisor of 1452)
...
1452 / 1451 = 1.0006891798759 (the remainder is 1, so 1451 is not a divisor of 1452)
1452 / 1452 = 1 (the remainder is 0, so 1452 is a divisor of 1452)

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 1452 (i.e. 38.105117766515). 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 $\frac{N}{d} = D$ )

1452 / 1 = 1452 (the remainder is 0, so 1 and 1452 are divisors of 1452)
1452 / 2 = 726 (the remainder is 0, so 2 and 726 are divisors of 1452)
1452 / 3 = 484 (the remainder is 0, so 3 and 484 are divisors of 1452)
...
1452 / 37 = 39.243243243243 (the remainder is 9, so 37 is not a divisor of 1452)
1452 / 38 = 38.210526315789 (the remainder is 8, so 38 is not a divisor of 1452)