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Using prime factorization to identify perfect squares.

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- 1. Using Prime Factorization to Identify Perfect Squares
- 2. What is Prime Factorization? Prime factorization is to write a composite number as a product of its prime factors. (www.northstarmath.com) Think back . . . A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or itself.
- 3. Example : What are the prime factors of 12? We can figure this out using a factor tree. 12 6 x 2 2 x 3 x 2 The prime factors of 12 are 2, 2 & 3!
- 4. Example : What are the prime factors of 48? 48 6 x 8 2 x 3 x 2 x 4 2 x 3 x 2 x 2 x 2 The prime factors of 48 are, 2, 2, 2, 2, & 3!
- 5. The prime factorization method can also be used to demonstrate that a number is not a perfect square. From the factor tree below, notice that none of the prime factors of 280 are present an even number of times. 280 10 x 28 2 x 5 x 2 x 14 2 x 5 x 2 x 2 x 7 280 = 2 x 2 x 2 x 5 x 7
- 6. A perfect square has each distinct prime factor occurring an even number of times.
- 7. Use the Prime Factorization Method to decide if 64 is a perfect square. 64 2 x 32 2 x 2 x 16 2 x 2 x 2 x 8 2 x 2 x 2 x 2 x 4 2 x 2 x 2 x 2 x 2 x 2 64 = 2 x 2 x 2 x 2 x 2 x 2 The factor 2 appears 6 times (an even number of time). We can say that 64 is a perfect square because . . .
- 8. A perfect square has each distinct prime factor occurring an even number of times.

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