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

*Consider the following factors and multiples by using division facts:***(i)**

15 is not completely divisible by 2

i.e., ** 14 ÷ 2 = 7 **or

When
a number (dividend) is completely divided by another number (divisor),
then this divisor is called a factor and the dividend is called a
multiple of the divisor.

Here 2 is the factor of the multiple 14.

14 ÷ 1 = 14, 14 ÷ 14 = 1, 14÷ 7 = 2

So the divisors 1, 14 and 7 are also the complete divisors or factors of the dividend (multiple) 14.

Thus, the factor must be a complete divisor of the multiple (dividend).

**(ii) **18 ÷ 2 = 9,

18 ÷ 3 = 6,

18 ÷ 9 = 2,

18÷ 6 = 3,

18 ÷ 1 = 18,

18 ÷ 18 = 1

If 18 are divided by 2, 3, 9, 6, 1 and 18, it is completely divided.

Thus, 2, 3, 9, 6, 1, 18 or 1, 2, 3, 6, 9 and 18 are the complete divisors or the factors of the multiple 18.

We may define a factor as the multiplier or complete divisor of its multiple.

A multiple has many but limited numbers of factors.

35 have 4 factors, i.e., 1, 5, 7 and 35.

42 have 8 factors, i.e., 1, 2, 3, 6, 7, 14, 21 and 42.

(iii) Let us find the factors of 24.

By division method

24 ÷ **1** = **24**

24 ÷ **2** = **12**

24 ÷ **3** = **8**

24 ÷ **4** = **6**

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

**Taking help of division to check multiples****(i)** Is 24 a multiple of 8? Use division.

24 ÷ 8 = 3 (No remainder)

Yes, 24 is a multiple of 8.

**(ii)** Is 56 a multiple of 5? Use division.

56 ÷ 5

Here remainder is 1

56 is not a multiple of 5 because there is a remainder.

**(iii)** Is 456 a multiple of 9? Use division.

456 ÷ 9

Here remainder is 6

456 is not a multiple of 9 because there is a remainder. **Note:**

In division if there is no remainder, the dividend is the multiple of the divisor.

**Finding the factors of a number through division****(i)** Take a look. Is 5 a factor of 15?

15 ÷ 5 = 3 15 ÷ 3 = 5

No remainder No remainder

5 is factor of 15. 3 is a factor of 15.

Both 3 and 5 are factor of 15.

**(ii)** Find the factors of 36:

1 × 36 = 36 2 × 18 = 36 3 × 12 = 36

4 × 9 = 36 5 is not a factor of 36 6 × 6 = 36

**Note:**

No need to do any more division because the factors are getting repeated.

Now we can write the factors like this:

**The factors of 36 are:**

**1 × 36 = 362 × 18 = 363 × 12 = 364 × 9 = 366 × 6 = 36**

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. **Note:**

It is very important to work systematically in math.

**(iii)** Is 7 a factor of 24?

24 ÷ 7 = 3 remainder 3

Here, remainder = 3

7 is not a factor of 24.

**Taking help of division to check multiples****(i)** Is 24 a multiple of 8? Use division.

24 ÷ 8 = 3 (No remainder)

Yes, 24 is a multiple of 8. **(ii)** Is 56 a multiple of 5? Use division.

56 ÷ 5

Here remainder is 1

56 is not a multiple of 5 because there is a remainder.

**(iii)** Is 456 a multiple of 9? Use division.

456 ÷ 9

Here remainder is 6

456 is not a multiple of 9 because there is a remainder.

**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**

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