Factors and Multiples of Whole Numbers F&P Math 10

Definitions to Know Prime Factorization – is the number written as a product of it’s prime factors Prime Factors – When a factor of a number has exactly two divisors, 1 and itself

Definitions to Know Composite Number – a number that is divisible by more than just 1 and itself Prime numbers are blue Composite numbers are orange

Prime Factoring Method #1 Factor Tree Branch into factors of the main number. Will branch out as you factor each side branch Keep going until you have reached a prime number on that branch Use exponents to show how many of each prime number you have factored Order from smallest to largest base

Practice – Factor Tree Method 3300 138

Prime Factoring Method #2 Hockey Stick or Division Table Only take our a prime factor at a time The left column will be all the prime factors The right column will be your composite that you continue until you have reached a prime in the right column Order from smallest to largest base

Practice – Hockey Stick Method 198 340

Choose A Method and Practice 27 36 685 1925

Why we need prime factors? GCF We use them to find the greatest common factor between multiple numbers Multiply only COMMON FACTORS together

Find the Greatest Common Factor (GCF) 90 and 225 154 and 198

Find the Greatest Common Factor (GCF) 245, 315, and 770 171, 285, and 399

Why we need prime factors? LCM We use them to find the lowest common multiple Multiply all factors, but take only the highest number of the factor

Find the Lowest Common Multiple (LCM) 15 and 35 126 and 441

Find the Lowest Common Multiple (LCM) 22, 154, and 198 58 and 124

Using Prime Factorization to Determine Perfect Square Is 256 a perfect square? Will result in two equal groups of prime factors

Using Prime Factorization to Determine Perfect Cube Is 512 a perfect cube? Will result in 3 equal groups of prime numbers

Today To Do: Start working through Prime Factorization worksheets Homework  30 minutes of working on worksheets at home over the weekend