What are the divisors of 4453?

1, 61, 73, 4453

There is a total of 4 positive divisors.
The sum of these divisors is 4588.
The arithmetic mean is 1147.

4 odd divisors

1, 61, 73, 4453

How to compute the divisors of 4453?

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 4453 by each of the numbers from 1 to 4453 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)

4453 / 1 = 4453 (the remainder is 0, so 1 is a divisor of 4453)
4453 / 2 = 2226.5 (the remainder is 1, so 2 is not a divisor of 4453)
4453 / 3 = 1484.3333333333 (the remainder is 1, so 3 is not a divisor of 4453)
...
4453 / 4452 = 1.0002246181491 (the remainder is 1, so 4452 is not a divisor of 4453)
4453 / 4453 = 1 (the remainder is 0, so 4453 is a divisor of 4453)

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 4453 (i.e. 66.730802482811). 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 $\frac{N}{d} = D$ )

4453 / 1 = 4453 (the remainder is 0, so 1 and 4453 are divisors of 4453)
4453 / 2 = 2226.5 (the remainder is 1, so 2 is not a divisor of 4453)
4453 / 3 = 1484.3333333333 (the remainder is 1, so 3 is not a divisor of 4453)
...
4453 / 65 = 68.507692307692 (the remainder is 33, so 65 is not a divisor of 4453)
4453 / 66 = 67.469696969697 (the remainder is 31, so 66 is not a divisor of 4453)