Prime Factor Tree

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 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 9 x 4 3 x 3 2 x 2 2 x 2 3 x 3 22 x 32 Let’s Choose a Number 36

4. 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! 3 x 12 3 x 6 x 2 3 x 2 x 3 x 2 2 x 2 x 3 x 3 22 x 32 Let’s Try That Again! 36

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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