Tables, multiples and factors
🎯 In this topic you will
- Recall and use multiplication facts for all times tables.
- Recognise factors and find the factors of a given number.
- Recognise multiples and find multiples of numbers.
🧠 Key Words
- array
- factor
- inverse operations
- multiple
- product
Show Definitions
- array: A way of arranging objects in equal rows and columns to represent multiplication.
- factor: A number that divides exactly into another number with no remainder.
- inverse operations: Operations that undo each other, such as multiplication and division.
- multiple: A number obtained by multiplying a given number by a whole number.
- product: The result of multiplying two or more numbers together.
Extending times table knowledge
In this section you will extend your knowledge of table facts to include the $7$ times table, and you will work out multiples and factors of whole numbers.
Sharing equally
The chocolate bar shown is made up of $28$ equal pieces. When the chocolate is shared so that everyone has the same number of pieces, both the number of people and the number of pieces each person gets must divide exactly into $28$.
Understanding factors
The number of people sharing the chocolate and the number of pieces they each receive are both factors of $28$. Factors always come in pairs and can be used to describe all the possible ways a number can be shared equally.
💡 Quick Math Tip
Finding factors: Factors always come in pairs. If one factor is small (like $1$, $2$, or $3$), the matching factor is found by dividing the number. When the pairs start repeating, you have found them all.
❓ EXERCISES
1. Helga is thinking of a $2$-digit number.
She says:
It is less than $3 \times 6$
It is more than $3 \times 5$
It is not equal to $2 \times 8$
What is Helga’s number?
👀 Show answer
2. Here is part of a number grid.
Which numbers are multiples of $7$?
👀 Show answer
3. Copy and complete this list of factors.
The factors of $32$ are $1$, _____, _____, _____, _____, $32$.
👀 Show answer
4. Bruno says, “The dates of all the Saturdays this month are $1$ less than a multiple of $7$”.
Is Bruno right?
Explain your answer.
👀 Show answer
5. Sam picks $50$ apples.
He packs all the apples into boxes.
He puts the same number of apples in each box.
How many boxes does Sam use?
Find different solutions.
👀 Show answer
6. Here are ten digit cards.
Use each card once to make five $2$-digit numbers that are multiples of $3$.
Ask your partner to check your answers.
Did you both make the same numbers?
👀 Show answer
7. Copy and complete the calculation so that the answer is a multiple of $8$.
$57 + \square = \square$
Can you find more than one answer?
👀 Show answer
8. Copy the Venn diagram and write the numbers in the correct place.
👀 Show answer
🧠 Think like a Mathematician
Here are four cards.
$3 \quad 4 \quad 5 \quad 6$
a. Place the cards in a square and multiply across the columns.
$4 \times 3 = 12$
$6 \times 5 = 30$
b. Move the cards and multiply again.
c. How many different products can you find?
You will show you are generalising when you recognise patterns in your results.
If you explain your results, you will show you are convincing.
Show Answers
- b. By rearranging the cards, different column pairs are formed, such as $3 \times 5 = 15$ and $4 \times 6 = 24$.
- c. Several different products are possible. The exact number depends on how the cards are paired in columns.
- Generalisation: Changing the order of numbers changes which pairs are multiplied, but the same numbers are always used.
💡 Quick Math Tip
Product meaning: The product is the result of a multiplication. For example, when you multiply two numbers, the answer you get is called the product.