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# Prime Factorization

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### Prime Factorization

1. 1. Prime Factor Tree
2. 2. Definitions <ul><li>Prime Number – An integer whose only factors are 1 and itself. </li></ul><ul><li>Factor – a number that can divide another number without a remainder. </li></ul><ul><li>Prime Factors – an expression of numbers that divides another integer without a remainder where all the factors are prime. </li></ul>
3. 3. Let’s Choose a Number <ul><li>Let’s use 36 </li></ul><ul><li>Choose any 2 factors – let’s use 9 and 4 </li></ul><ul><li>Now let’s factor these numbers, too </li></ul><ul><li>Next, arrange them from least to greatest </li></ul><ul><li>Last, re-write as exponents </li></ul>36 4 9 x 2 2 x x 3 3 2 2 x 3 2 2 2 3 3 x x
4. 4. Let’s Try That Again! <ul><li>Let’s use 36 again </li></ul><ul><li>Choose any 2 factors – let’s use 3 and 12 </li></ul><ul><li>Now let’s factor these numbers, too </li></ul><ul><li>Oops, 6 is not prime - let’s factor again! </li></ul><ul><li>Next, arrange them from least to greatest </li></ul><ul><li>Last, re-write as exponents </li></ul><ul><li>Look, it’s the same answer! </li></ul>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. 5. Let’s Re-Cap <ul><li>Composite numbers are made up of factors </li></ul><ul><li>In a Prime Factor Tree, the goal is to keep reducing each factor to its lowest possible prime factors </li></ul><ul><li>When you have all the prime factors identified, re-arrange them from least to greatest and re-write them as exponents </li></ul>