If you multiply a number by another number, the answer you get is called the product. The number being multiplied is called the multiplicand and the number multiplied is called the multiplier. Here, multiplicand and multiplier are the factors of the product. Students can learn about factors and multiples using the multiplication facts on this page.

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## Factors and Multiples by using Multiplication Facts

Multiplication is one of the basic arithmetic operations which is expressed as the repeated addition in short. Representing two numbers as a product is called the multiplication fact. We generally use the cross (x) symbol for multiplication. Any multiple has a finite number of factors.

Multiplication fact formula is multiplicand x multiplier = product or factor x factor = multiple. The numbers that are multiplied are called the factors of the multiple. Let us have a look at the examples for a better understanding.

**Examples:**

Multiply 4 by 7

4 x 7 = 28

4, 7 are the factors of multiple 28

Multiply 8 by 6

8 x 6 = 48

Here, 8 is the multiplicand, 6 is multiplier, and 48 is product

8, 6 are the factors of multiple 48

### How to find Factors and Multiples Using Multiplication Facts?

Follow the simple guidelines to calculate the multiples and factors using multiplication facts and they are along the lines:

**Factors**

- Write the multiple numbers.
- Next, multiply the multiple by 1.
- Get any two multiples of the multiple.
- Repeat step 3 to get the numbers that can not be further divided.
- The obtained multiples are called the factors of multiple.

**Multiple**

- List the factors of the number.
- Multiply all the factors.
- The obtained product is called the multiple.

### Using Multiplication Facts to find Factors and Multiples Examples

**Question 1:**

Find the factors of the multiple 48 by using 12 x 4 = 48

**Solution:**

Given multiplication fact is 12 x 4 = 48

By observing the question, 12 and 4 are the factors of 48

Using the multiplication method, 48 can be written as

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

So, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 6, 24, and 48.

**Question 2:**

Find the factors of the multiple 150 using 5 x 30 = 150

**Solution:**

Given multiplication fact is 5 x 30 = 150

By observing the multiplication fact, the factors of 150 are 30, 5

Using the multiplication method, 150 can be written as

1 x 150 = 150

3 x 50 = 150

5 x 30 = 150

6 x 25 = 150

10 x 15 = 150

So, the factors of 150 are 1, 3, 5, 6, 10, 15, 25, 30, and 150.

**Question 3:**

Find the multiplication fact for each division fact and write the factors of the multiple.

(i) 8 ÷ 1 = 8

(ii) 96 ÷ 12 = 8

(iii) 55 ÷ 5 = 11

**Solution:**

(i) Given division fact is 8 ÷ 1 = 8

The multiplication facts are 8 x 1 = 8, 1 x 8 = 8

Find the factors of 8 using the multiplication method.

1 x 8 = 8

2 x 4 = 8

4 x 2 = 8

8 x 1 = 8

Therefore, the factors of multiple 8 are 1, 2, 4, 8

(ii) Given division fact is 96 ÷ 12 = 8

The multiplication facts are 12 x 8 = 96, 8 x 12 = 96

Find the factors of multiple 96

1 x 96 = 96

2 x 48 = 96

3 x 32 = 96

4 x 24 = 96

6 x 16 = 96

8 x 12 = 96

12 x 8 = 96

16 x 6 = 96

24 x 4 = 96

32 x 3 = 96

48 x 2 = 96

96 x 1 = 96

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

(iii) Given division fact is 55 ÷ 5 = 11

The multiplication facts are 5 x 11 = 55, 11 x 5 = 55

Find the factors of multiple 55

1 x 55 = 55

5 x 11 = 55

11 x 5 = 55

55 x 1 = 55

Therefore, the factors of 55 are 1, 5, 11, and 55.

### Frequently Asked Question’s

**1. What are factors in multiplication?**

In a multiplication, the number that we multiply is called the fcators of the product. For example, 2 multipled by 3 gets 6 as product. 2 x 3 = 6, here 2 and 3 are factors of 6.

**2. How do you explain factors and multiples?**

A multiple is a number that can be divided by another number a certain number of times without remainder. A factor is a number that divides the multiple completely.

**3. How many multiplication facts can we get from a division fact?**

We can write exactly two multiplication facts for each division fact.