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Multiples and Factors
Multiples
• A multiple is formed by multiplying a given number by the counting numbers.
• The counting numbers are 1, 2, 3, 4, 5, 6, etc.
Example: List the multiples of 4:
• 4 x 1 = 4
• 4 x 2 = 8
• 4 x 3 = 12
• 4 x 4 = 16
• 4 x 5 = 20
• 4 x 6 = 24
Counting Numbers
So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.
What are the first five multiples of 13?
13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
13 x 5 = 65
13, 26, 39, 52, 65
Find the Missing Multiples
• 6, 12, 18, ____, ____
• ___, 6, 9, 12, ____, ____, 21
• ___, 24, 36, 48, 60, ____
24 30
3 15 18
12 72
MENTAL MATH
• Find the first 5 multiples of the following numbers
• a) 4 ____, _____, _____, _____, ____
• b) 5 ____, _____, _____, _____, ____
• c) 8 ____, _____, _____, _____, ____
• d) 15 ____, _____, _____, _____, ____
• e) 20 ____, _____, _____, _____, ____
REMEMBER! • Factors are the numbers you multiply
together to get a product.
• For example, the product 24 has several factors.
• 24 = 1 x 24
• 24 = 2 x 12
• 24 = 3 x 8
• 24 = 4 x 6
• The factors are 1, 2, 3, 4, 6, 8, 12, 24
Decomposing Factors
1. Factor Tree
2. Break the numbers down into the primefactors that make them up.
Step 1 Write the number you are going to break down
90Step 2 Plot a vertical line at the right side of
the number
90
Step 3 Write the smallest prime that divides the number. Start with number 2 and
continue with 3, 5 and son on.
• Half of 90 is 45
• 90 divided by 2 is 45
90 245
Can you divide 45 by 2 with no remainder?
•90 2 45 3 15 3 5
• Continue with the next prime number that is 3.
•90 2 45 3 15 3 5 5 1
• Continue with the next prime number that is 5.
Step 4 Repeat the same procedure until the quotient is 1
Let´s try together
120 2 Write the smallest prime
that divides the number. Start with number 2.
HALF OF 120
Let´s try together
120 260
What is the smallest prime that divides 60?
Let´s try together120 2 60 2 30
What is the smallest prime that divides 30?
HALF OF 30
Let´s try together120 2 60 2 30 2 15
What is the smallest prime that divides 15?
HALF OF 15 WITH NO REMAINDER?
Let´s try together120 2 60 2 30 2 15 3 5
What is the smallest prime that divides 5?
What is the next prime number?
Let´s try together120 2 60 2 30 2 15 3 5 5 1
HOW DO YOU EXPRESS IT?
• 2 X 2 X 2 X 3 X 5 = 120
• 2 X 3 X 5
HELP YOUR TEACHER!!
72
60
TIME TO PRACTICE
Break the following numbers down
45 126 28
Break the following numbers down
20 27 45 20 27 45