The document explains the concept of prime factorization and outlines how to create a prime factor tree using examples with the number 36. It describes selecting factors, breaking them down into their prime components, and rearranging the prime factors as exponents. Additionally, it mentions that the content is part of a free educational resource available online.

1. Prime Factor Tree Discovering Prime Factors of Any Number

2. Definitions Prime Number – An integer whose only factors are 1 and itself. Factor – a number that can divide another number without a remainder. Prime Factors – an expression of numbers that divides another integer without a remainder where all the factors are prime.

3. Let’s Choose a Number Let’s use 36 Choose any 2 factors – let’s use 9 and 4 Now let’s factor these numbers, too Next, arrange them from least to greatest Last, re-write as exponents 36 4 9 x 2 2 x x 3 3 2 2 x 3 2 2 2 3 3 x x

4. Let’s Try That Again! Let’s use 36 again Choose any 2 factors – let’s use 3 and 12 Now let’s factor these numbers, too Oops, 6 is not prime - let’s factor again! Next, arrange them from least to greatest Last, re-write as exponents Look, it’s the same answer! 36 3 x x 2 6 12 3 x 3 x x 3 2 2 x 2 x 3 x x 2 3 2 2 x 3 2

5. Let’s Re-Cap Composite numbers are made up of factors In a Prime Factor Tree, the goal is to keep reducing each factor to its lowest possible prime factors When you have all the prime factors identified, re-arrange them from least to greatest and re-write them as exponents

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