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

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

4. 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.

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

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

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

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

10. 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.

12. Greatest common factor is sometimes called greatest common divisor.

13. #1 Write the prime factorization of each
number without exponents
#2 Circle the common factors
#3 Multiply them together from one of the
numbers

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

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

16. 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 𝑎𝑛𝑑 𝑥 3 𝑦
# 𝑚 𝑎𝑛𝑑 𝑚 2
# 𝑥 𝑎𝑛𝑑 𝑥 3

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