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Bell Ringer • What is a prime number? • What is a composite number? • Give an example of each. Greatest Common Factor Mr. Haupt CC.2.1.8.E.1 Greatest Common Factor • The Greatest Common Factor, or GCF, is the largest number that goes in to every number given. • For example, the GCF of 12 and 16 is 4. • To find the GCF, you need to know the difference between prime and composite numbers. Prime Numbers • Prime numbers are numbers where the only factors, or ways to multiply, are one and the given number. • For example, the number 17 can only be broken down into one times 17. • Other examples: 1, 2, 3, 5, 7, 11, 13, 19, 23, 31, etc… Composite Numbers • Composite numbers are basically numbers that are not prime. • So, they are numbers that have more multiples than just one and itself. • For example, the factors of 28 are: • 1 x 28 • 2 x 14 • 4x7 Prime or Composite? • 89 • 21 • 33 • 97 Prime Factorization • Prime Factorization is breaking a number down into its smallest (prime number) factors. • I find it easiest to use a factor tree. • 30 54 What if we add letters? • Nothing changes, except now we have to write out the letters. • 45a2b3 36c3d GCF, finally! • So finally, we can get to the actual GCF. • To find the GCF, we have to do the prime factorization of each number given. • Then we take all the prime numbers they have in common, and multiply them. • Our answer is the GCF. For example… • Find the GCF: • 36 and 45 • 28a2b and 35ab2 A few more… • 88 and 44 • 64a2b2 and 96a2b
