TT6 week 11 lessons 43-45

Chapter 8

Lessons 43-45

Factors

A factor of a number is a number that divides the given number evenly or exactly, leaving no remainder.
Eg. 2 and 3 are factors of 6.

Finding the factors

1. know your multiplication tables

2. know your divisibility rules

Example

What numbers can you multiply together to equal 20? What are the factors of 20?

Multiple Choice

What are all the factors of 18?

• 1, 3, 6, 12, 15, 18

• 1, 2, 3, 6, 9, 18

• 2, 3, 5, 7, 14

• 1, 2, 4, 5, 10, 18

Multiple Choice

What are all the factors of 42?

• 10, 20, 30, 40
• 1, 2, 3, 6, 7, 14, 21, 42

• 1, 2, 3, 4, 5, 6, 7, 8
• 2, 3, 5, 7, 11, 13

Multiple Choice

True or false:

The factors of a number are all of the whole numbers that will divide it evenly.

• true

• false

Multiple Choice

True or false:

The factors of a number always include the number 1 and itself.

• True

• False

Multiple Select

Which of the following are factors of 21?

• 4

• 7

• 1

• 3

• 21

Greatest common factor (GCF)

The Greatest Common Factor is the largest factor that any two numbers have in common. This is useful to know when reducing fractions or simplifying equations. Knowing the GCF will help you create equivalent fractions as well. We will get to that later.

Finding the GCF: Method 1

Make a list of all the factors for each number and find the largest one they both have.

Finding the GCF: Method 2

Factor both numbers down to prime numbers. If they share 2 prime number factors, multiply those numbers to get the GCF.

If they share only 1 number, that number is the GCF.
If they share no numbers, 1 is the GCF.

What factors do 8 and 12 have in common?

Multiple Choice

True or false:

two factors are called "common" when they are plain and uninteresting.

• True

• False

Multiple Choice

True or false:

The GCF is the largest whole number that is a factor of two (or more) numbers. i.e. it is shared between two or more numbers.

• true

• false

Match

Match each number pair to its GCF.

• 4, 12

• 10, 15

• 8, 16

• 6, 9

4

5

8

3

• 4

• 5

• 8

• 3

Using the GCF to reduce fractions

We can use the GCF to reduce fractions. Just as we found equivalent fractions by multiplying or dividing the numerator and denominator by the same number, we can fully reduce a fraction all the way down to its simplest form by using the GCF.

Math Response

Find the GCF and reduce

$$\frac{21}{35}$$

Use the fraction icon next to the X symbol to enter your answer.

Type answer here

Correct Answer: \frac{3}{5}

Deg^°

Rad

Math Response

Find the GCF and reduce:

$$\frac{12}{18}$$

Type answer here

Correct Answer: \frac{2}{3}

Deg^°

Rad

Multiple Choice

A fraction that cannot be simplified or reduced any further is considered fully reduced (or reduced to lowest terms).

• true

• false

Prime numbers

Prime numbers are numbers that are only divisible by 1 and themselves. Eg, 3 is only divisible by 1 or 3, therefore it is prime.

There are a lot of prime numbers. We use them when we factor numbers to find

​Memorizing prime numbers can save you time in math. Or you could just add the chart to your notes. ;)

​We use prime factorization in math to simplify expressions or equations quickly.

Composite numbers

A composite number is a positive integer greater than 1 that has more than two factors. Unlike prime numbers, which are only divisible by 1 and themselves, composite numbers can be divided evenly by other numbers. The smallest composite number is 4, and examples include 6 (divisible by 1, 2, 3, and 6) and 9 (divisible by 1, 3, and 9).  

Multiple Choice

Is this number prime or composite?
23

• Prime
• Composite

Multiple Choice

Is this number prime or composite?
25

• Prime
• Composite

Multiple Select

Which of the following are prime numbers

• 6
• 17

• 2

• 4

Multiple Choice

What are the prime factors of 42?

• 1, 2, 21
• 2, 3, 7

• 3, 17, 41

• 6, 7, 12

Multiple Choice

What are all prime numbers divisable by?

• 1, 2, and itself
• 1 and itself
• Every number from 1-10
• They aren't divisable at all

Homework

Homework: Chapter 8 lessons 43-45.

Math lab today 2:30-3:30 in Google.