What are the divisors of 4452?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 53, 84, 106, 159, 212, 318, 371, 636, 742, 1113, 1484, 2226, 4452

There is a total of 24 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 504.

16 even divisors

2, 4, 6, 12, 14, 28, 42, 84, 106, 212, 318, 636, 742, 1484, 2226, 4452

8 odd divisors

1, 3, 7, 21, 53, 159, 371, 1113

How to compute the divisors of 4452?

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 4452 by each of the numbers from 1 to 4452 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)

4452 / 1 = 4452 (the remainder is 0, so 1 is a divisor of 4452)
4452 / 2 = 2226 (the remainder is 0, so 2 is a divisor of 4452)
4452 / 3 = 1484 (the remainder is 0, so 3 is a divisor of 4452)
...
4452 / 4451 = 1.0002246686138 (the remainder is 1, so 4451 is not a divisor of 4452)
4452 / 4452 = 1 (the remainder is 0, so 4452 is a divisor of 4452)

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 4452 (i.e. 66.723309270449). 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 $\frac{N}{d} = D$ )

4452 / 1 = 4452 (the remainder is 0, so 1 and 4452 are divisors of 4452)
4452 / 2 = 2226 (the remainder is 0, so 2 and 2226 are divisors of 4452)
4452 / 3 = 1484 (the remainder is 0, so 3 and 1484 are divisors of 4452)
...
4452 / 65 = 68.492307692308 (the remainder is 32, so 65 is not a divisor of 4452)
4452 / 66 = 67.454545454545 (the remainder is 30, so 66 is not a divisor of 4452)