5th Grade Factors and Multiples | Definitions | Solved Examples

Here we will discuss how factors and multiples are related to each other in math.

Factors of a Number:

A number that divides a given number exactly is called the factor of the given number.

For example:

40 ÷ 1 = 40 The remainder is 0, so 1 and 40 are factors.

40 ÷ 2 = 20 : The remainder is 0, so 2 and 20 are factors.

40 ÷ 5 = 8: The remainder is 0, so 5 and 8 are factors.

40 ÷ 10 = 4 : The remainder is 0, so 10 and 4 are factors.

40 ÷ 20 = 2 The remainder is 0, so 20 and 2 are factors.

Hence, factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

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

Thus, we observe the following facts about factors:

✅ Every natural number can be divided by 1, so 1 is a factor of all natural numbers

✅ Every natural number can be divided by itself, so every natural number is a factor of itself.

✅ Factors of a number are either smaller or equal to the number.

✅ As a factor is less than or equal the number, so there are definite number of factors of a given number.

✅ If two numbers are factors of each other, they should be equal.

Definition of Factor:

A factor of a number is a divisor which divides the dividend exactly.

For example,

2 is a factor of 6, 3 is a factor of 12 etc.

Let us consider some more examples.

1. Write all the factors of 36.

Solution:

All the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

A factor of a number which is a prime number is called a prime factor.

For example, 3 is a prime factor of 36.

2. Find the prime factor of 312.

Solution:

Therefore, the prime factors of 312 are 2 x 2 x 2 x 3 x 13.

Multiples of a Number:

When a number divides another number exactly, the second number is called the multiple of first one.

In other words, a multiple of a number is the product of that number and any natural number.

For example:

Multiples of 2 are: 2 x 1 = 2

                           2 x 2 = 4

                           2 x 3 = 6

                           2 x 4 = 8

                           2 x 5 = 10

                           .     .     .

                           .     .     .

                           .     .     .

                           and so on.

Multiples of 6 are: 6 x 1 = 6

                           6 x 2 = 12

                           6 x 3 = 18

                           6 x 4 = 24

                           6 x 5 = 30

                           .     .     .

                           .     .     .

                           .     .     .

                           and so on.

To find multiples of a number, multiply the given number by natural numbers.

Thus, we observe the following facts about multiples:

✅ Every number is a multiple of itself.

✅ Every number is the smallest multiple of itself.

✅ Every number is a multiple of 1.

✅ Every multiple of a number is either greater than or equal to the number.

✅ There are infinite number of multiples of a number.

Whenever a number is divided by another number leaving no remainder, then the divisor is called the factor of the dividend, and the dividend is the multiple of the divisor.

Definition of Multiple:

A multiple of a number is the product of the number and a whole number.

For example, multiples of 4 are 4, 8, 12, 16, 20, etc.

Here 4 is the product of 4 and 1.

Similarly, 8 is the product of 4 and 2 and 12 is the product of 4 and 3 and so on.

Let us consider an example.

1. Find the first five multiples of 24 except itself.

Solution:

The first five multiples of 24 are

24 x 2 = 48,

24 x 3 = 72,

24 x 4 = 96,

24 x 5 = 120,

24 x 6 = 144

Remember:

The factors of a number are always limited but the multiples of a number are unlimited.

For example, 16 has only 5 factors 1, 2, 4, 8, 16 but its multiples are unlimited — 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, …

Worksheet on 5th Grade Factors and Multiples

I. Find all the factors of the following other than 1.

1. 36

2. 48

3. 64

4. 75

5. 124

6. 150

7. 169

8. 175

9. 210

Answer:

I. 1. 2, 3, 4, 6, 9, 12, 18, 36

2. 2, 3, 4, 6, 8, 12, 16, 24, 48

3. 2, 4, 8, 16, 32, 64

4. 5, 15, 25, 75

5. 2, 4, 31, 62, 124

6. 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

7. 13, 169

8. 5, 7, 25, 35, 175

9. 3, 5, 7, 10, 15, 21, 30, 35, 70, 105, 210

II. Find the prime factors of following numbers.

1. 27

2. 77

3.40

4. 63

5. 143

6. 75

7. 100

8. 185

9. 196

Answer:

II. 1. 3

2. 7, 11

3. 2, 5

4. 3, 7

5. 11, 13

6. 3, 5

7. 2, 5

8. 5, 37

9. 2, 7

III. Find the first six multiples of each number (excluding the number itself).

1. 4

2. 8

3. 12

4. 8

5. 15

6. 17

Answer:

III. 1. 8, 12, 16, 20, 24, 28

2. 16, 24, 32, 40, 48, 56

3. 24, 36, 48, 60, 72, 84

4. 16, 24, 32, 40, 48, 56

5. 30, 45, 60, 75, 90, 105

6. 34, 51, 68, 85, 102, 119

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