Properties of Numbers Need white copy paper for double bubbles.

Multiples and Factors

Learning Goals Identify prime, composite, square, even and odd numbers. Determine if one number is a factor or a multiple of another number Identify and learn multiplication combinations

Factors 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 SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24

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.

4 × 5 = 20 Factors Multiple

Let’s name the first five multiples: 3: 6: 7: 4: GLASS MODE

What are the factors of 7? The only factors of 7 are 1,7 1 x 7 2 x ?? 3 x ?? 4 x ?? 5 x ?? 6 x ?? 7 x 1 This works, but it is a repeat. We are done.

Find the Missing Multiples 24 30 6, 12, 18, ____, ____ ___, 6, 9, 12, ____, ____, 21 ___, 24, 36, 48, 60, ____ 15 18 3 72 12

Integers Answer these: Write down the factors of: a) 15 b) 64 c) 48 d) 32 e) 72 f) 84 2. Write down the first 5 multiples of a) 3 b) 2 c) 5 d) 13 e) 15 f) 16 1, 3, 5, 15 1, 2, 4, 8, 16, 32, 64 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 1, 2, 4, 8, 16, 32 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 3, 6, 9, 12, 15 2, 4, 6, 8, 10 5, 10, 15, 20, 25 13, 26, 39, 52, 65 15, 30, 45, 60, 75 16, 32, 48, 64, 80

Lowest Common Multiple (LCM) To find the lowest common multiple of two numbers, simply list the multiple of each number and the first number that appears in both lists is the LCM. e.g. Find the LCM of 8 and 14 8 16 24 32 40 48 56 64 72 80 14 28 42 56 70 84 56 is the first number to appear in each list and so 56 is the LCM

LCM and HCF Harder Questions A farmer has 24 cows and 30 sheep. She decides to divide these equally between her sons. What is the greatest number of sons she can have? HCF question: List the factors of both: 24 1 2 3 4 6 8 12 30 1 2 3 5 6 10 15 Number of sons she can have is 6

Homework Time Math Makes Sense Textbook – pg 44; Q’s 1, 2, 5, 8

Prime and Composite Numbers have more than two factors. EXAMPLES: 6, 18, 30, 100 Prime numbers are numbers that only have two factors: one, and the number itself. EXAMPLES: 3, 5, 7, 11, 31

Which list contains all prime numbers? 1, 2, 3, 7 2, 3, 7, 13 11, 13, 9, 17 21, 23, 37, 41 GLASS MODE

Let’s review what we’ve learned How can you know if a number is a prime number? How can an array help you identify a square number? What is a factor? What is a strategy you can use to find all the factors of a given number? Glass mode: Who can write an equation for this array? Who can write it with more than 2 factors?

Guiding Question How are multiples different from factors?

Discussion What do you think? Did you find any “favorite” strategy that helped you, that you could share with the rest of us? Which ones did you find most challenging? Did any of your puzzles have more than one answer? Or no answer?

Let’s Review our Guiding Questions What are multiples? How are multiples different from factors? Share Take a few minutes to answer these in your journal.

Journal Time 1, 6, 20, 2, 12, 3, 4, 9, 16, 5, 11, 28, 25 From this list of numbers, write down: The prime numbers The multiples of 4 The factors of 6 Square Numbers (You might use some numbers more than once) Complete the Number Line handout for factors & multiples