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Let’s learn about prime factorization.
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Let's review some vocabulary.
prime number: any positive integer with EXACTLY two factors is a prime number, 1 and itself
factors: the numbers you multiply together to get the product— algebraically it would look like this
- a • b = c where a and b are the factors and c is the product
composite number: positive integers that have THREE or more whole number factors
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What if you want to find all of the factors of a number? How could you do it? EASY! Use Prime Factorization! In fact, get out your Sieve of Eratosthenes to help you. This is a great tool because it can help provide a way for you to check for prime numbers.
Prime Factorization is a method used to find all of the prime factors of a number. It utilizes a tree diagram for organizing your factors.
Let’s try it using the number 24.
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Step 1: Make a tree
- Start by writing the number and then drawing two tree branches underneath.
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Step 2: Begin factoring…
- Think of the factors of the number (or, if this seems hard, think, "What can I divide this number evenly by?" since sometimes it is easier to think backwards). Write down the two numbers at the end of the tree branches.
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- Keep factoring the numbers…until you get down to prime numbers.
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- In this next example, you will see how the numbers 4 and 6 have been factored further until we get down to the primes.
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Step 3: Circle the Prime Numbers
- When you get to the prime factors, circle them.
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Step 4: Write the Prime Numbers using Exponents
- Re-write the prime numbers as an expression, using exponents. Voila!
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If you want even MORE practice, then click More Prime Factorization Practice.
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