Greatest common factor Mr. Hendy Industries

WALT: Find the Greatest Common Factor between different numbers Learning goal WALT: Find the Greatest Common Factor between different numbers

Two methods for finding the gcf Factor Search Prime Factorization List factors 24: 1, 2, 3, 4, 6, 8, 12, 24 36: 1, 2, 3, 4, 5, 6, 9, 12, 18, 36 GCF = 12 Factor trees for both numbers, then multiply prime numbers Prime factors for 24 and 36 24: 2 x 2 x 2 x 3 36: 2 x 2 x 3 x 3 GCF = 2 x 2 x 3 = 12

Factor search

Step #1: list the factors What numbers can we multiply together to equal our base number? What factors does our base number have? 12: 1, 2, 3, 4, 6, 12

Step #2: Circle the largest factor that both numbers have in common 12: 1, 2, 3, 4, 6, 12 24: 1, 2, 3, 4, 6, 8, 12, 24

GCF = 12 Step #3: record the gcf 12: 1, 2, 3, 4, 6, 12 After you have listed all the factors for your numbers and circled the Greatest Common Factor (GCF), record the GCF 12: 1, 2, 3, 4, 6, 12 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF = 12

Some examples Find the GCF of 20 and 30

Some examples Find the GCF of 17 and 25

Some examples Find the GCF of 15, 45, and 30

Challenge!

Challenge! 15 and 33 15 and 33

Challenge! Gcf = 3 15 and 33 15 and 33

Challenge!

Challenge! 40 and 18 40 and 18

Challenge! Gcf = 2 40 and 18 40 and 18

Consolidation 10 and 25 42 and 16 36 and 21 5 and 40 18 and 54 Find the GCF for the following sets of numbers 10 and 25 42 and 16 36 and 21 5 and 40 18 and 54 24, 12 and 36

Consolidation 10 and 25 GCF = 5 42 and 16 GCF = 2

Consolidation 36 and 21 GCF = 3 5 and 40 GCF = 5

Consolidation 18 and 54 GCF = 18 24, 12, and 36 GCF = 12

Success criteria I am successful when I can…

Finding GCF using Prime Factorization But wait! There’s more… Finding GCF using Prime Factorization

Step #1: create a factor tree for your numbers 12 24 2 6 3 2 12 2 6 3 2 2

Step #2: List out all prime factors 12: 2 x 2 x 3 24: 2 x 2 x 2 x 3

Step #3: circle each pair of identical prime factors 12: 2 x 2 x 3 24: 2 x 2 x 2 x 3

Step #4: multiply the prime factors together to get your gcf 2 x 2 x 3 = 12 Therefore the GCF between 12 and 24 is 12

Lowest Common Multiple Mr. Hendy Industries

WALT: Find the Lowest Common Multiple between numbers Learning goal WALT: Find the Lowest Common Multiple between numbers

What is a multiple? 5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 Let’s say we start with the number 5. Every time we multiply 5 by another number, we create a MULTIPLE. Watch… 5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 Therefore: 5, 10, 15, 20, 25 are multiples of 5

Lowest common multiple To find the Lowest Common Multiple between numbers, we need to list multiples for both numbers until we find one that is the same between them. For example… 4: 4, 8, 12, 16, 20 5: 5, 10, 15, 20

Some examples Find the LCM of 15 and 4

Some examples Find the LCM of 15 and 4 LCM = 60

Some examples Find the LCM of 13 and 16

Some examples Find the LCM of 13 and 16 LCM = 208

Find the LCM of the following numbers practice Find the LCM of the following numbers 8 and 6 12 and 6 7 and 15 9 and 6 13 and 18 20 and 45

Consolidation 8 and 16 LCM = 16 12 and 6 LCM = 12

Consolidation 7 and 15 LCM = 105 9 and 6 LCM = 18

Consolidation 13 and 18 LCM = 234 20 and 45 LCM = 180

Success criteria I am successful when I can…