Counting by Multiples

Find Multiples and Factors

Find Multiples and Factors

Presenter

Dr. Luis Bello

[e-mail]

Source:

https://openstax.org/books/prealgebra-2e/pages/2-4-find-multiples-and-factors

Learning Objectives

• Identify multiples of numbers

• Use common divisibility tests

• Find all the factors of a number

• Identify prime and composite numbers

Identify Multiples of Numbers

Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn’t have to count each one. She counts by twos:

2,4,6,8,10,12.

She has 12 shoes in her closet.

The numbers 2,4,6,8,10,12 are called multiples of 2.

Multiples of 2 can be written as the product of a counting number and 2.

The first six multiples of 2

are given below.

1⋅2=2

2⋅2=4

3⋅2=6

4⋅2=8

5⋅2=10

6⋅2=12

Divisibility Tests

A number is divisible by

2 if the last digit is 0,2,4,6,or8

3 if the sum of the digits is divisible by 3

5 if the last digit is 5 or 0

6 if divisible by both 2 and 3

10 if the last digit is 0

How To

Find all the factors of a counting number.

Step 1. Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.

If the quotient is a counting number, the divisor and quotient are a pair of factors.

If the quotient is not a counting number, the divisor is not a factor. If the quotient is a counting number, the divisor and quotient are a pair of factors. If the quotient is not a counting number, the divisor is not a factor.

Step 2. List all the factor pairs.

Step 3. Write all the factors in order from smallest to largest.

Find all the factors of 72.

Identify Prime and Composite Numbers

Some numbers, like 72,

have many factors. Other numbers, such as 7,

have only two factors: 1and the number.

A number with only two factors is called a prime number. A number with more than two factors is called a composite number.

The number 1 is neither prime nor composite. It has only one factor, itself.

Prime Numbers and Composite Numbers

A prime number is a counting number greater than 1whose only factors are 1 and itself.

A composite number is a counting number that is not prime.

How To Determine if a number is prime.

Step 1. Test each of the primes, in order, to see if it is a factor of the number.

Step 2. Start with 2 and stop when the quotient is smaller than the divisor or when a prime factor is found.

Step 3. If the number has a prime factor, then it is a composite number. If it has no prime factors, then the number is prime.

Multiple Choice

Is 3 a factor of 12?

• yes

• no

Multiple Choice

Find the prime number.

• 10
• 9
• 7
• 4

Multiple Choice

Which of the following is a multiple of 7?

• 28
• 48
• 71
• 45

Multiple Choice

Joe has listed the first 4 multiples of 7 as: 
7   14    22     28
Which one is incorrect?

• 7
• 14
• 22
• 28

Multiple Choice

Which number is NOT prime?

• 3
• 7
• 17
• 21

Multiple Choice

A prime number is...

• a number that has only one factor.
• a number that has at least two factors.
• a number that has more than two factors.
• a number that has only two factors.
  (1 and itself)

Multiple Choice

Which is a NOT a factor of 9?

• 0
• 1
• 3
• 9

Multiple Choice

Which number is a factor of 24

• 9
• 7
• 11
• 12

Multiple Choice

Which number is a factor of 10

• 3
• 4
• 5
• 8

Multiple Choice

List the first (4) multiples of 8

• 1, 2, 4, 8

• 8, 16, 24, 32

Multiple Choice

Choose a COMPOSITE number

• 1

• 2

• 3

• 12

Multiple Select

Choose all the PRIME numbers

• 1

• 2

• 3

• 5

Multiple Choice

TRUE or FALSE?

A FACTOR is greater than the number you are factoring

• TRUE

• FALSE

Multiple Choice

TRUE or FALSE?

A FACTOR is greater than the number you are factoring

• TRUE

• FALSE