010r. Factors and Multiples

Learning Intentions

• To know what factors and multiples are
• To understand that each number has infinitely many multiples
• Solve factors of a number
• find multiples of a number

Pre-requisite Summary

• Understanding multiplication and division
• Knowledge of basic multiplication tables
• Ability to perform simple division and Check remainders
• Understanding of even and odd numbers
• Familiarity with prime and composite numbers

Worked Examples

Worked Example 1

Identify factors:

a) Factors of

b) Factors of

Worked Example 2

Identify multiples:

a) First five multiples of

b) First five multiples of

Worked Example 3

Check if a number is a factor:

a) Is a factor of ?

b) Is a factor of ?

Worked Example 4

Check if a number is a multiple:

a) Is a multiple of ?

b) Is a multiple of ?

Problems

Problem 1

a) Find all factors of

b) Find all factors of

Problem 2

a) List the first five multiples of

b) List the first five multiples of

Problem 3

a) Is a factor of ?

b) Is a factor of ?

Problem 4

a) Is a multiple of ?

b) Is a multiple of ?

Exercises

Understanding and Fluency

Exercise 1.

Find factors:

a)

b)

c)

Exercise 2.

List multiples:

a) First five multiples of

b) First five multiples of

c) First five multiples of

Exercise 3.

Determine if a number is a factor:

a) a factor of

b) a factor of

c) a factor of

Exercise 4.

Determine if a number is a multiple:

a) a multiple of

b) a multiple of

c) a multiple of

Exercise 5.

Mixed practice:

a) Factors of

b) Multiples of

c) Check if is a factor of

Reasoning

Exercise 6.

Explain why has more factors than .

Exercise 7.

How do you know that a number has infinitely many multiples?

Exercise 8.

Compare factors and multiples of and .

Exercise 9.

Why is a factor of every number?

Exercise 10.

Can a prime number have more than two factors? Explain.

Problem-solving

Exercise 11.

Find two numbers that have exactly the same set of factors.

Exercise 12.

Find the first multiple of greater than .

Exercise 13.

A gardener plants flowers in rows of and . Find a number of flowers that could make complete rows for both.

Exercise 14.

A bus arrives every minutes, and a train every minutes. After how many minutes will they both arrive together?

Exercise 15.

Find all numbers less than that are multiples of and .

Potential Misunderstandings

• Students may confuse factors and multiples
• Students may think a number has only a limited number of multiples
• Students may miss some factors if they stop checking early
• Students may assume all multiples are smaller than the number
• Students may forget that and the number itself are always factors
• Students may confuse prime numbers with numbers having many factors

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