Factors and multiples by using multiplication facts are explained here. With the help of this operation we shall learn some other terms.

*Consider the following factors and multiples by using multiplication facts: *

(i) 3 × 5 = 15,

i.e., 3 multiplied by 5 gives the product 15.

Here, 3 is called the **multiplicand**, 5 is the **multiplier** and 15 is the **product**.

In 5 × 3 = 15, 5 is the multiplicand and 3 is the multiplier.

Thus, in any multiplication fact, multiplicand and multiplier may be interchanged. Both are known as **factors**. We can say 3 and 5 are the factors of 15. The product 15 may also be given the name of ‘multiple’. Thus, 15 is the multiple of the factors 3 and 5.

(ii) 1 × 15 = 15.

Here, 1 and 15 are the factors of multiple 15.

Thus, the multiple 15 has four factors, 1, 3, 5 and 15.

(iii) 1 × 3 × 5 = 15.

It also expresses that 1, 3 and 5 are the factors of 15.

(iv) 4 × 3 = 12,

i.e., 4 multiplied by 3 gives the product 12. We can say 4 and 3 are the factors of multiple 12.

Accordingly, 2 × 2 × 3 = 12, where 2, 2 and 3 are the factors of multiple 12.

also 1 × 2 × 2 × 3 = 12.

So 1, 2, 2 and 3 are the factors of 12.

1 × 2 × 6 = 12, **or**, 1 × 4 × 3 = 12 shows that 1, 2, 4, 6 are the factors of 12.

1 × 12 = 12

So, 1 and 12 are the factors of 12.

Hence, 1, 2, 3, 4, 6 and 12 are the** factors of the multiple 12**.

There are no other factors except 1, 2, 3, 4, 6 and 12 of multiple 12.

Any multiple has a definite number of factors.

12 has 6 factors, i.e., 1, 2, 3, 4, 6 and 12.

15 has 4 factors, i.e., 1, 3, 5 and 15.

**More explanation:**

David has 8 marbles. Let us see in how many ways David can arrange these marbles.

The division facts for each of the multiplication facts are:

8 ÷ 1 = 8

8 ÷ 8 = 1

8 ÷ 2 = 4

8 ÷ 4 = 2

So, 8 is exactly divisible by 1, 2, 4 and 8.Therefore, 1, 2, 4 and 8 are factors of 8. A number is a factor of another number if it is an exact divisor of the number. We can find factors of a number by multiplication or by division method.

**How to find the factors with the help of multiplication facts?**

**Using multiplication facts,**

**(i) Factor Factor Multiple **

** 7 × 9 = 63**

**(ii) Factor Factor Multiple**

** 8 × 4 = 32**

**(iii) Factor Factor Multiple**

** 6 × 5 = 30**

We learnt that the product of the two numbers is the multiple of each of the numbers.

**In other words:** each of the numbers is the factor of the multiple.

(i) 7 and 9 are factors of 63

(ii) 8 and 4 are factors of 32

(iii) 6 and 5 are factors of 30**Note:**

Any number which can be divided into a bigger number without leaving a remainder is a factor of the bigger number.

**● **Let us find the factors of 24 by multiplication method.

**1** × **24** = 24

**2** × **12** = 24

**3** × **8** = 24

**4** × **6** = 24

**1**, **2**, **3**, **4**, **6**, **8**, **12** and **24** are the factors of 24

**● **Find all the factors of 64 by multiplication method.

64 = **1** × **64**

64 = **2** × **32**

64 = **4** × **16**

64 = **8** × **8**

Hence, all the factors of 64 are** 1**,** 2**,** 4**,** 8**,** 16**,** 32**,** 64**.

**Related Concept**

**● ****Factors
and Multiples by using Multiplication Facts**

**● ****Factors
and Multiples by using Division Facts**

**● ****Factors**

**● ****Even
and Odd Numbers Between 1 and 100**

**● ****Examples
on Even and Odd Numbers**

**4th Grade Math Activities**

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