The Fundamental Theorem of Arithmetic states that any composite number (number divisible by more than two dividers) , is a product of prime numbers. So, in this article you will learn how to do prime factorization. This decomposition will allow then calculate the lcm (least common multiple) and gcd (greatest common divisor).
Prime Factorization method
With this two examples we will explain how to make the prime factorization (decomposition into prime factors).
Taking one of the examples :
- Check if the number is divisible by the first prime number, 2. If so, perform the division (12: 2 = 6). If not, see if it is divisible by the following prime number, and so on, until you find a prime number that is a divisor of the given number. To do this step is important to know the divisibility rules.
- Repeat the same procedure until you have the result 1.
- The number you want to decompose is the product of all prime numbers placed to the right of the line.
The tree method
In this method of prime factorization, you will decompose the given number, until you have only prime numbers. Look at the example.
We hope that this article was helpfull to you learn how to do prime factorization and study maths.