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Unit 2: Understanding Positive Real Numbers Lesson 3: Factors and Prime Factorization Vocabulary: 1. factor – whole numbers that are multiplied to find a product (Ex. The “factors” of 12 are 1, 2, 3, 4, 6, and 12.) 2. prime factorization – a number written as the product of its prime factors (Ex. The “prime factorization” of 12 is 2 x 2 x 3.) 3. divisible- when a number is able to be evenly divided by another number with a remainder of zero. 4. composite number- numbers that are divisible by more than two numbers. 5. prime number- a number that is divisible by only the numbers 1 and itself. A number is divisible by… 2 if the last digit is even 3 if the sum of the digits is divisible by 3 4 if the last two digits form a number divisible by 4 5 if the last digit is 0 or 5 6 if the number is divisible by both 2 and 3 9 if the sum of the digits is divisible by 9 10 if the last digit is 0 Divisibility Rules Divisible 3,978 315 (3 + 1 + 5 = 9) 8,512 Not Divisible 4,975 139 (1 + 3 + 9 = 13) 7,518 14,975 48 711 (7 + 1 + 1 = 9) 15,990 Checking Divisibility 10,978 20 93 (9 + 3 = 12) 10,536 TRY THESE: Tell whether 610 is divisible by 2, 3, 4, and 5. ______________________ Tell whether 387 is divisible by 6, 9, and 10. _______________________ Identifying Prime and Composite Numbers Tell whether each number is prime or composite. A. 45 B. 13 C. 19 D. 49 Finding Factors *We are Factor Ninjas! We have come to FLMS to chop numbers into smaller numbers (their factors)! * *Helpful Hint: When finding factors, use your math facts! Start with one and the number itself. Then build up from one (2, 3, 4…). Once you get to a math fact that repeats factors you’ve already used, you are done. Example 1A: List all of the factors of: Example 1B: List all of the factors of: 18 1 * 18 2*9 3*6 *4 and 5 are not factors of 18, and 6 would repeat, so you are done!* Now, in a U direction, list the numbers. The factors will be written in order from least to greatest! 24 1 * 24 2 * 12 3*8 4*6 *5 is not a factor of 24, and 6 would repeat, so you are done!* Now, in a U direction, list the numbers. The factors will be written in order from least to greatest! TRY THESE: List the factors of the following number: 1. 12: ______________________________________________________________ 2. 21: ______________________________________________________________ 3. 52: ______________________________________________________________ 4. 75: ______________________________________________________________ Writing Prime Factorization Method: Ladder Diagram *This method involves dividing your number by prime factors. Step 1: Divide 30 by a prime number. Step 2: Divide that quotient by another prime number. Step 3: Keep dividing until you get 1 for a quotient. Step 4: The prime numbers on the outside of the ladder are all the prime factors of that number. Using those prime factors, write a multiplication problem with the numbers written from least to greatest. *Remember: all factors in prime factorization MUST be PRIME!* TRY THESE: Use the ladder method to find the prime factorization of the following numbers: 1.) 14 2.) 18 3.) 63 4.) 54