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.
7 and 8 are the factors. 56 is their product.
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.
Multiplication can also describe equal groups. For example, 4 × 3 = 12 can represent four groups containing three objects in each group.
Understanding what the factors and product represent makes it easier to connect one multiplication fact with another.
Factors, Products and the × Symbol
Three simple terms describe the different parts of a multiplication equation.
The numbers being multiplied are called factors.
The result of multiplying the factors is called the product.
The multiplication symbol is commonly read as “times” or “multiplied by.”
The complete equation connects the two factors with their product.
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.
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.
Any number multiplied by zero has a product of zero.
Multiplying a number by one leaves the number unchanged.
Turnaround Multiplication Facts
Reversing the order of two factors does not change their product. This is the commutative property of multiplication.
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.
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.
Six groups of seven give a product of 42.
Reversing the factors keeps the same product.
Dividing the product by one factor gives the other.
The relationship works with either factor.
For two different nonzero factors, one multiplication fact can be connected with its turnaround fact and two corresponding division equations.
Patterns in Multiplication Facts
Several times tables have properties that make their products easier to recognize or check.
If at least one whole-number factor is even, the product is even.
Whole-number multiples of 5 end in 0 or 5.
Positive whole-number multiples of 10 end in 0.
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.
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.
5 × 7 = 35. Add one more 7: 35 + 7 = 42.
4 × 8 = 32. Double the product: 32 × 2 = 64.
10 × 7 = 70. Subtract one 7: 70 − 7 = 63.
If 6 × 8 = 48 is known, the commutative property gives 8 × 6 = 48.
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
If 4 × 8 = 32, what is 8 × 4? Reveal
If 10 × 7 = 70, what is 9 × 7? Reveal
If 6 × 9 = 54, what is 54 ÷ 9? Reveal
Which square fact has a product of 64? Reveal
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 →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
2. Connect it to an easier fact Link
3. Hide the answer Recall
4. Mix the facts Practice
5. Return to difficult facts Focus
For a complete learning sequence, see How to Learn Times Tables.
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.