Transcript Greatest Common Factor

Annual Garage Sale
Ever since last year’s community garage sale. Kyle has
been saving $2 coins, $5 bills and $10 bills. Now he has
$30 worth of each. He is looking forward to buying
some items at this year’s sale.
What prices can Kyle pay for exactly, using only $2 coins,
$5 bills and $10 bills?
A. What can Kyle pay for using only $2 coins?
B. What can he pay for using only $5 bills?
C. What can he pay for using only $10 bills?
D. Which prices require Kyle to use more than one type of
bill or coin? Explain why?
E. Write a price that is greater than $100 and that
someone can pay using only one type of bill or coin.
F. Write a price that is greater than $100 and that
someone cannot pay using only one type of bill or coin.
Scooter
$30
Skateboard
$22
Baseball
Glove
$15
Snowboard
$59
Do You Remember?
•
A bag of marbles can be divided evenly among two, three or four friends.
A) How many marbles might be in the bag?
B) What is the least number of marbles that can be in the bag?
C) How many marbles would there be if there are between 30 and 40
marbles in the bag?
How many marbles would each friend get? Use a diagram or another
strategy to show your answer.
2. Suppose that you have three different lengths of linking cubes, as show
below. Assume that you have as many of these lengths as you need, but
you may not take them apart.
Can you make each length below using only one colour? If it is possible, show
more than one way
a) 25 cubes
b) 20 cubes
c) 18 cubes
d) 29 cubes
e) 30 cubes
f) 32 cubes
Do You Remember? : The Sequel
3. Find all the possible whole number lengths and widths of rectangles with
each area given below. You might draw on centimetre grid paper or use
another strategy.
•
12 cm2
•
20 cm2
•
17 cm2
•
24 cm2
Factors are whole numbers (not including 0) that
are multiplied together to give a product
- divides into another whole number with no
remainder
Sometimes represented by F(x) or F(X)
Factoring – is breaking a number down into all its
factors
Examples
Find the factors of the following numbers
a). 5 = 5x1 F(5) = 1, 5
k). 24 =3x8, 1x24
12x2, 6x4,
b). 30 = 5x6, 1x30, 15x2 l). 32=32x1, 8x4
3x10
16x2
c). 42 = 14x3, 1x42, 2x21
m). 4 =2x2, 1x4
7x6.
d). 12= 1x12, 4x3, 6x2 n). 13= 1x13
e). 8 = 4x2, 8x1
o). 22= 11x2, 1x22
f). 15 = 5x3, 1x15
p). 6 = 2x3, 1x6
g). 36 =9x4, 6x6, 18x2, q). 9 = 3x3, 1x9
= 36x1, 3x12
The Greatest Common Factor (GCF) is the largest factor
that divides all the numbers
To find the Greatest Common Factor (GCF) of two numbers:
1. List all the factors of each number
2. If there are no common factors, the GCF is 1
For Example
F(18) = 1, 2, 3, 6, 9, 18
F(24) = 1, 2, 3, 4, 6, 8, 12, 24
The GCF is 6
F(25) = 1, 5, 25
F(17) = 1, 17
The GCF is 1
Homework Sept 30
Find the Greatest Common Factor of each.
1. 12 & 15
2.
3.
4.
5.
4&9
16 & 24
30 & 18
12, 30 & 9
F(12) = 1, 2, 3,4, 6, 12 The GCF = 3
F(15) = 1, 3, 5, 15
Multiples is the product of a number and any other whole number.
-Zero (0) is a multiple of every number
-A product is the answer to a multiplication question
- Sometimes represented by M(x) or M(x)
For Example
Multiples of 4: M(4); 4, 8, 12, 16, 20, 24 … (4x1), (4x2), (4x3), (4x4), (4x5), …
Multiples of 6: M(6): 6, 12, 18, 24, …
A common multiple of 4 and 6 is 24
(6x1), (6x2), (6x3), (6x4), (6x5), …
The Lowest Common Multiple (LCM) of two numbers is the
smallest number (not zero) that is a multiple of all numbers.
To find the LCM of two numbers:
1. List the multiples of each number.
2. Sometimes, the LCM will be the numbers multiplied together.
For Example:
M(2) = 2, 4, 6, 8, 10,12, …
M(3) = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …
M(3) = 3, 6, 9, 12, 15, …
M(8) = 8, 16, 24, 32 40, 48 …
The LCM = 6
The LCM = 24