Section 4.3 Prime Factorization and Greatest Common Divisor Algebra Concepts Section 4.3 Prime Factorization and Greatest Common Divisor

Prime number- integer greater than 1 with exactly two factors, 1 and the number itself.

http://www.youtube.com/watch?v=cRz4hW9SPPc

Composite number- an integer greater than 1 with more than two positive factors. There are an infinite number of prime numbers and an infinite number of composite numbers.

Prime factorization- writing a composite number as a product of prime numbers.

Use a factor tree to find the prime factorization of a number.

Try these- make a factor tree and write the prime factorization #1 230 #2 344 #3 64 #4 900 #5 75

Common factors- factors that two or more numbers have in common.

Greatest common factor- the largest factor of all the common factors of two or more numbers. Two or more numbers always have the factor “1” in common because 1 is a factor of all numbers.

Greatest common factor is sometimes called greatest common divisor.

#1 Write the prime factorization of each number without exponents #2 Circle the common factors #3 Multiply them together from one of the numbers

Find the GCF #1 30 and 45 #2 60 and 30 #3 66 and 32

Sometimes there are variables involved. The procedure is the same.

Find the GCF #1 20 𝑥 2 𝑦 2 𝑎𝑛𝑑 35 𝑥 3 𝑦 #2 44 𝑚 3 𝑎𝑛𝑑 32 𝑚 2 #1 20 𝑥 2 𝑦 2 𝑎𝑛𝑑 35 𝑥 3 𝑦 #2 44 𝑚 3 𝑎𝑛𝑑 32 𝑚 2 #3 12 𝑥 4 𝑎𝑛𝑑 9 𝑥 3

Relatively prime numbers- two numbers that have a GCF of 1