Common multiple and factors
🎯 In this topic you will
- Find common multiples of numbers.
- Find common factors of numbers.
🧠 Key Words
- common factor
- common multiple
- factor
- multiple
Show Definitions
- common factor: A number that is a factor of two or more numbers.
- common multiple: A number that is a multiple of two or more numbers.
- factor: A whole number that divides another number exactly with no remainder.
- multiple: A number made by multiplying a given number by a whole number.
🍫 Sharing a Chocolate Bar
Imagine you have this bar of chocolate. You divide it between you and your friends so you all have the same number of pieces.
👥 Equal Groups of Pieces
You can divide it equally between 2 people, 3 people, 4 people, 6 people, 8 people, 12 people or 24 people.
🔢 Understanding a Common Multiple
We say that 24 is a common multiple of 2, 3, 4, 6, 8, 12 and 24.
🎯 What You Will Learn Next
In this section you will learn about common multiples and common factors.
❓ EXERCISES
$1$. Write the numbers in the correct place on a copy of the Venn diagram.
$5,\ 14,\ 15,\ 18,\ 20,\ 21,\ 24,\ 29,\ 30,\ 60$
Which numbers are common multiples of $2$, $3$ and $5$?
Discuss your answer with your partner. Do you agree with each other?
👀 Show answer
Placement in the Venn diagram:
Multiples of $2$ only: $14$
Multiples of $3$ only: $21$
Multiples of $5$ only: $5$
Multiples of $2$ and $3$ only: $18,\ 24$
Multiples of $2$ and $5$ only: $20$
Multiples of $3$ and $5$ only: $15$
Multiples of $2$, $3$ and $5$: $30,\ 60$
Outside all circles: $29$
$2$. The numbers in this sequence increase by $3$ each time.
$3, 6, 9, 12, \ldots$
The numbers in this sequence increase by $5$ each time.
$5, 10, 15, 20, \ldots$
Both sequences continue.
Write a number bigger than $100$ which is in both sequences.
👀 Show answer
$3$. Write all the common multiples of $3$ and $8$ that are less than $50$.
👀 Show answer
$4$. Olivia and Amir play football regularly.
Olivia plays once every $4$ days.
Amir plays once every $3$ days.
If they both play football today, how many times in the next fortnight will they play on the same day?
👀 Show answer
$5$.
a. Write the factors of $18$.
b. Write the factors of $24$.
c. Draw a ring around the common factors.
👀 Show answer
a. Factors of $18$: $1,\ 2,\ 3,\ 6,\ 9,\ 18$
b. Factors of $24$: $1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24$
c. Common factors: $1,\ 2,\ 3,\ 6$
$6$. Write all the factors of $30$ that are also factors of $20$.
👀 Show answer
$7$. Pierre gives $32$ football cards to his friends.
He shares them equally so all his friends have the same amount.
How many friends could Pierre have? Explain your answer.
👀 Show answer
$8$. Isabella has three digit cards.
Which two cards could she use to make:
a. a common multiple of $5$ and $13$?
b. a common factor of $60$ and $90$?
👀 Show answer
a. Use the $6$ and $5$ cards to make $65$, which is a common multiple of $5$ and $13$.
b. Use the $1$ and $5$ cards to make $15$, which is a common factor of $60$ and $90$.
🧠 Think like a Mathematician
The sequence $4, 2, 1, 3$ uses the numbers $1$ to $4$ so that each number is either a factor or a multiple of the previous number.
Each number is used once only.
Find a similar sequence that uses the numbers $1$ to $6$.
Tip
Use digit cards that you can easily move around.
👀 show answer
One possible sequence is: $4, 2, 6, 3, 1, 5$
Check: $2$ is a factor of $4$, $6$ is a multiple of $2$, $3$ is a factor of $6$, $1$ is a factor of $3$, and $5$ is a multiple of $1$.