Check For Ugly Number In Python

You might have heard about natural numbers, prime numbers, even numbers, and odd numbers. But, have you ever wondered what an ugly number is? In this article, we will discuss what an ugly number is. We will also write a program to check for an ugly number in python.

What Is An Ugly Number?

A number is said to be an ugly number if it has only 2,3, and 5 as its prime factors. In other words, If a number can be obtained by multiplying powers for 2, 3, or 5, the number is said to be an ugly number. 

For instance, 18 can be obtained as 2¹x 3². Hence, it is an ugly number. Similarly, 90 is also an ugly number as it can be obtained as 2¹x 3²x 5¹. On the contrary, 126 is not an ugly number as it can be obtained as 2¹x 3²x 7¹. Here, 126 has 7 as one of its prime factors. Hence, it is not an ugly number.

Now, let us formulate an algorithm to check for an ugly number in Python.

Algorithm To Check For Ugly Number In Python

To check if a number is an ugly number or not, we will perform repetitive division on it. First, we will divide the given number repeatedly with 2. If the resultant number becomes indivisible by 2, we will check if the number is 1 or not. If it’s 1, we will say that a number is an ugly number. Otherwise, we will perform repetitive division on the resultant by 3. Once the resultant becomes indivisible by 3, we will check if it’s 1 or not. If yes, we will say that the given number is an ugly number. Otherwise, we will perform repetitive division on the resultant by 5. Once the resultant becomes indivisible by 5, we will check if the resultant is 1. If yes, we will say that a number is an ugly number. Otherwise, we will say that the number is not an ugly number.

Let us now implement this idea in Python

Python Program To Check For Ugly Number

Here, we have implemented a function is_ugly() using the while loop for repetitive division and if-else statements for condition checking. The function takes an integer as an input argument and returns True if the input number is an ugly number. Otherwise, it returns False.

def is_ugly(N):
    while N % 2 == 0:
        N = N // 2
    if N == 1:
        return True
    while N % 3 == 0:
        N = N // 3
    if N == 1:
        return True
    while N % 5 == 0:
        N = N // 5
    if N == 1:
        return True
    return False


input_number = 18
output = is_ugly(input_number)
print("{} is an ugly number:{}".format(input_number, output))
input_number = 126
output = is_ugly(input_number)
print("{} is an ugly number:{}".format(input_number, output))

Output:

18 is an ugly number:True
126 is an ugly number:False

Conclusion

In this article, we have discussed and implemented a program to check whether a given number is an ugly number or not. To learn more about numbers in python, you can read this article on decimal numbers in python. You might also like this article on complex numbers in python.