Prime factorization by the factor tree method is a way to break down a composite number into its prime factors. Here's how it works:
Start with the Number: Begin with the composite number you want to factorize.
Find Two Factors: Look for any two numbers that multiply together to give you the original number.
Draw a Branch for Each Factor: Once you've found two factors, draw branches stemming from the original number, with each branch representing one of the factors.
Repeat the Process: If any of the factors on the branches are still composite numbers (i.e., not prime), repeat the process for each of them. Continue breaking down each composite number into its factors until all branches lead to prime numbers.
Continue Until Prime: Keep repeating the process until all branches of the factor tree lead to prime numbers.
Read the Result: Once you've reached a point where every branch ends with a prime number, the prime factorization of the original number is the multiplication of all these primes.
For example, let's say you want to find the prime factorization of 24:
Start with 24.
You can break it down into 2 and 12.
12 can be further broken down into 2 and 6.
6 can be broken down into 2 and 3.
Now, you have reached prime numbers (2, 2, 2, and 3).
This method is useful for finding the prime factors of large numbers and understanding their fundamental building blocks.
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