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Prime Factors

Prime Factors. Prime and Composite Numbers, Prime Factorization, GCF & LCM. Checklist Points. Understand the difference between a prime and composite number . You will be able to find the lowest common multiple and greatest common factor of a set of numbers. What are Factors?.

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Prime Factors

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  1. Prime Factors Prime and Composite Numbers, Prime Factorization, GCF & LCM.

  2. Checklist Points • Understand the difference between a prime and composite number. • You will be able to find the lowest common multiple and greatest common factor of a set of numbers.

  3. What are Factors?

  4. Prime Numbers • A prime number is defined as a whole number which has exactly two factors. The two factors are always one and the number itself. Ex) What are the factors of 3, 7 and 11?

  5. Composite Numbers • A composite number is a whole number which has more than two factors. Ex) What are the factors of 10 and 18? • Note: the number 1 has only one factor and is neither prime nor composite

  6. Prime Factors • The prime factors of a whole number are the factors of the number which are prime For example: The factors of 6 are 1, 2, 3, and 6. The prime factors of 6 are 2 and 3 ( because 1and 6 are not prime). DO: • State the factors of 12. • State the prime factors of 12.

  7. Prime Factorization • A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. [see Thiessen text pg 90 for more detail] • A small number can be factored in our heads but for larger numbers a tree diagram can be used.

  8. Factor Trees Find the prime factors of 48.

  9. Examples Find the prime factors of the following using the factor tree method. • 15 b) 66 c) 24 d)12

  10. GCF & LCM QUESTION: What is the difference between a factor and a multiple? Video: Factors and Multiples • Give me an example of a factor of 15. • Give me an example of a multiple of 15.

  11. Greatest Common Factor • The greatest common factor (GCF) of a set of whole numbers is the largest whole number which divides exactly into each of the numbers in the set. • We will use our knowledge of prime factorization to determine the GCF of two numbers.

  12. Steps to find GCF • Factor each value using the factor tree. • Circle the prime numbers that are common between the two numbers you are factoring. • Multiply one set of those numbers to find your GCF Example:

  13. Example #2 Find the greatest common factor of 48 and 64.

  14. Example #3 Find the greatest common factor of 27, 90, 84.

  15. Least Common Multiple • A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 12, 24, .... • The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. The least common multiple of 3 and 4 is 12. • Ex) Multiples of 12 are…12,24,36,48,60,72,….Multiples of 18 are…18,36,54,72,90,108,…The smallest multiple the 2 numbers have in common is the least common multiple, which is 36

  16. Steps to Find LCM • Factor each value using the factor tree. • Write down the numbers they have in common only once (GCF), then write down the leftover numbers. • Multiply them all together. **Easiest way to find the lcm is to use the chart shown in finding GCF

  17. Examples Find the greatest common factor and lowest common multiple of 2940 and 3150. • Next Step: Put into chart

  18. GCF: Factors that are common between both numbers LCM: Factors that are present in either/both numbers, but DO NOT DUPLICATE

  19. Find the lowest common multiple between 22, 154, and 198

  20. Assignment 1) find the GCF of the following sets of numbers: • a) 12, 3 • b) 16, 28 • c) 40, 26 • d) 48, 54, 2) In the Thiessen textbook page 93, part C do the following questions: 1, 3, 6, 8, 9, 12

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