Multiplication basics

Multiplication Facts

Multiplication facts are equations such as 6 × 4 = 24 and 8 × 7 = 56 that connect two factors with their product.

Explore the multiplication facts from 1 to 12, learn the vocabulary behind them, and discover how properties, fact families and number patterns connect facts that may initially seem unrelated.

ANATOMY OF A MULTIPLICATION FACT
7 × 8 = 56

7 and 8 are the factors. 56 is their product.

3 × 4 = 12 6 × 7 = 42 9 × 8 = 72
Start with the definition

What Is a Multiplication Fact?

A multiplication fact is an equation that states the product of two factors. Basic multiplication facts are the equations learners repeatedly use when working with multiplication.

3 × 4 = 12
6 × 7 = 42
9 × 8 = 72

Multiplication can also describe equal groups. For example, 4 × 3 = 12 can represent four groups containing three objects in each group.

×
A fact is more than an answer to memorize

Understanding what the factors and product represent makes it easier to connect one multiplication fact with another.

Multiplication vocabulary

Factors, Products and the × Symbol

Three simple terms describe the different parts of a multiplication equation.

6×8
EXAMPLE 6 × 8 = 48
FACTORS 6 and 8

The numbers being multiplied are called factors.

PRODUCT 48

The result of multiplying the factors is called the product.

SYMBOL ×

The multiplication symbol is commonly read as “times” or “multiplied by.”

COMPLETE FACT 6 × 8 = 48

The complete equation connects the two factors with their product.

Essential reference

Multiplication Facts From 1 to 12

Choose a number to explore its multiplication facts from ×1 through ×12, together with patterns and calculation strategies for that table.

Prefer to see many facts at once? The multiplication chart arranges the products in a grid so relationships between different tables are easier to compare.

Two fundamental facts

What Happens When You Multiply by 0 or 1?

Multiplication by zero and multiplication by one follow two important rules that apply to every number.

ZERO PROPERTY 8 × 0 = 0

Any number multiplied by zero has a product of zero.

IDENTITY PROPERTY 8 × 1 = 8

Multiplying a number by one leaves the number unchanged.

0·1
REMEMBER ×0 gives 0. ×1 keeps the original number.
One fact, two orders

Turnaround Multiplication Facts

Reversing the order of two factors does not change their product. This is the commutative property of multiplication.

3 × 8 24
8 × 3 24
Same product ✓
↔
a × b = b × a

Knowing 7 × 8 = 56 also gives you 8 × 7 = 56.

This relationship is especially easy to see on a multiplication chart, where matching products appear on opposite sides of the main diagonal.

Multiplication and division

What Is a Multiplication Fact Family?

Multiplication and division are inverse operations. The same three numbers can therefore appear in a group of related multiplication and division equations.

MULTIPLICATION 6 × 7 = 42

Six groups of seven give a product of 42.

TURNAROUND FACT 7 × 6 = 42

Reversing the factors keeps the same product.

RELATED DIVISION 42 ÷ 6 = 7

Dividing the product by one factor gives the other.

RELATED DIVISION 42 ÷ 7 = 6

The relationship works with either factor.

4
Four related equations

For two different nonzero factors, one multiplication fact can be connected with its turnaround fact and two corresponding division equations.

Recognize relationships

Patterns in Multiplication Facts

Several times tables have properties that make their products easier to recognize or check.

EVEN FACTORS 2, 4, 6, 8...

If at least one whole-number factor is even, the product is even.

MULTIPLES OF 5 5, 10, 15, 20...

Whole-number multiples of 5 end in 0 or 5.

MULTIPLES OF 10 10, 20, 30, 40...

Positive whole-number multiples of 10 end in 0.

SQUARE FACTS 8 × 8 = 64

When the two factors are equal, their product is a square number.

Square facts include 4 × 4 = 16, 6 × 6 = 36, 8 × 8 = 64 and 12 × 12 = 144. See the square numbers guide for a closer look at this pattern.

Use what you already know

Build New Facts From Known Facts

A fact you already know can become an anchor for another multiplication fact. This is useful when the new product is not yet easy to recall.

ADD ONE GROUP 5 × 7 → 6 × 7

5 × 7 = 35. Add one more 7: 35 + 7 = 42.

DOUBLE 4 × 8 → 8 × 8

4 × 8 = 32. Double the product: 32 × 2 = 64.

SUBTRACT ONE GROUP 10 × 7 → 9 × 7

10 × 7 = 70. Subtract one 7: 70 − 7 = 63.

TURN IT AROUND 6 × 8 → 8 × 6

If 6 × 8 = 48 is known, the commutative property gives 8 × 6 = 48.

Check your understanding

Can You Connect These Multiplication Facts?

Try each question before revealing the answer. These questions test the relationships between facts rather than simply presenting them in order.

If 5 × 7 = 35, what is 6 × 7? Reveal
Add one more group of 7: 35 + 7 = 42. Therefore, 6 × 7 = 42.
If 4 × 8 = 32, what is 8 × 4? Reveal
Reverse the factors. The product does not change, so 8 × 4 = 32.
If 10 × 7 = 70, what is 9 × 7? Reveal
Subtract one group of 7: 70 − 7 = 63. Therefore, 9 × 7 = 63.
If 6 × 9 = 54, what is 54 ÷ 9? Reveal
Multiplication and division are inverse operations, so 54 ÷ 9 = 6.
Which square fact has a product of 64? Reveal
8 × 8 = 64.
Move from understanding to recall

Practice Random Multiplication Facts

Once you understand how multiplication facts are connected, practice them in mixed order so you cannot rely on the sequence of a single table.

Practice multiplication facts →
Develop recall

How to Remember Multiplication Facts

Calculation strategies are useful while a fact is being learned. With practice, the goal is to retrieve familiar products accurately without working through every intermediate step.

1. Understand the fact Start
Make sure you know what the factors and product represent instead of treating the equation as an unrelated string of numbers.
2. Connect it to an easier fact Link
Use doubling, a turnaround fact, ×10 minus one group, or another nearby fact when useful.
3. Hide the answer Recall
Look at the two factors and attempt to retrieve the product before checking the answer.
4. Mix the facts Practice
Practice different multiplication tables together instead of always answering one sequence from beginning to end.
5. Return to difficult facts Focus
Give additional practice to facts that you miss or that still require several calculation steps.

For a complete learning sequence, see How to Learn Times Tables.

Quick answers

Multiplication Facts Questions

What is a multiplication fact?

A multiplication fact is an equation showing two factors and their product, such as 7 × 6 = 42.

What are factors in multiplication?

Factors are the numbers being multiplied. In 7 × 8 = 56, 7 and 8 are the factors.

What is a product in multiplication?

The product is the result of multiplication. In 7 × 8 = 56, the product is 56.

Why is 7 × 8 the same as 8 × 7?

Multiplication is commutative. Reversing the order of the factors does not change their product, so both equations equal 56.

What happens when a number is multiplied by zero?

The product is zero. For example, 12 × 0 = 0.

What is a multiplication fact family?

A multiplication and division fact family contains related equations using the same factors and product. For example: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

What is a square multiplication fact?

A square fact multiplies a number by itself. Examples include 5 × 5 = 25, 8 × 8 = 64 and 12 × 12 = 144.

Put the facts into practice

Ready to Practice Multiplication?

Answer multiplication facts from different tables in mixed order and strengthen the products that take you longer to recall.

INTERACTIVE PRACTICE Practice Multiplication Facts