Transcript Factors and Multiples

Properties of Numbers
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
6
Let’s name the first five multiples:
• 3:
• 6:
• 7:
• 4:
What are the factors of 7?
1x7
The only factors of 7 are 1,7
2 x ??
3 x ??
4 x ??
5 x ??
6 x ??
7x1
This works, but it is a repeat. We are done.
Find the Missing Multiples
24
30
• 6, 12, 18, ____, ____
15
18
• ___, 6, 9, 12, ____, ____, 21
3
72
• ___, 24, 36, 48, 60, ____
12
Integers
Answer these:
1. Write down the factors of:
a) 15
1, 3, 5, 15
b) 64
1, 2, 4, 8, 16, 32, 64
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
c) 48
d) 32
1, 2, 4, 8, 16, 32
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
e) 72
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
f) 84
2. Write down the first 5 multiples of
a) 3 3, 6, 9, 12, 15
b) 2 2, 4, 6, 8, 10
c) 5 5, 10, 15, 20, 25
d) 13 13, 26, 39, 52, 65
e) 15 15, 30, 45, 60, 75
f) 16 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
24
30
1
2
3
5
6
10
15
30
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
Prime numbers are
numbers that only have
two factors: one, and the
number itself.
EXAMPLES:
3, 5, 7, 11, 31
Composite numbers
have more than two
factors.
EXAMPLES:
6, 18, 30, 100
Which list contains all prime
numbers?
A.
B.
C.
D.
1, 2, 3, 7
2, 3, 7, 13
11, 13, 9, 17
21, 23, 37, 41
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?
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?
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