# Python Challenges: Get the Hamming numbers upto a given numbers also check whether a given number is a Hamming number

## Python Challenges - 1: Exercise-25 with Solution

Write a Python program to get the Hamming numbers upto a given numbers also check whether a given number is a Hamming number.

Hamming numbers are numbers of the form

H = 2^{i} x 3^{j} x 5^{k}

Where i, j, k ≥ 0

The sequence of Hamming numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27. . . consists of all numbers of the form 2i.3j.5k where i, j and k are non-negative integers.

**Explanation:**

**Sample Solution**:

**Python Code:**

```
def is_hamming_numbers(x):
if x == 1:
return 1
if x % 2 == 0:
return is_hamming_numbers(x/2)
if x % 3 == 0:
return is_hamming_numbers(x/3)
if x % 5 == 0:
return is_hamming_numbers(x/5)
return 0
def hamming_numbers_sequence(x):
if x == 1:
return 1
hamming_numbers_sequence(x-1)
if is_hamming_numbers(x) == True:
print("%s" % x, end=' ')
print(is_hamming_numbers(7))
print(is_hamming_numbers(1))
hamming_numbers_sequence(24)
print()
```

Sample Output:

0 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24

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