Important Formulas: Number System
Number system is the foundation of mathematics and plays a crucial role in various mathematical operations. Here are some important formulas related to the number system:

1. Divisibility Rules:
- A number is divisible by 2 if its last digit is even.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
- A number is divisible by 5 if its last digit is 0 or 5.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 9 if the sum of its digits is divisible by 9.

2. Prime Numbers:
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- Examples of prime numbers include 2, 3, 5, 7, 11, 13, etc.

3. Factorization:
- Factorization is the process of finding the factors of a given number.
- For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

4. LCM (Least Common Multiple) and HCF (Highest Common Factor):
- LCM is the smallest multiple that is divisible by two or more numbers.
- HCF is the largest number that divides two or more numbers without leaving a remainder.

5. Squares and Cubes:
- The square of a number is obtained by multiplying the number by itself.
- The cube of a number is obtained by multiplying the number by itself twice.
By understanding and applying these formulas, you can solve various number system problems efficiently and accurately.