Maths

Factors and Multiples

Class 4

🎯 Learning Objectives

📖 Let Us Begin!

Imagine you have 12 laddoos and you want to arrange them in equal rows. You can make 1 row of 12, 2 rows of 6, 3 rows of 4, 4 rows of 3, 6 rows of 2, or 12 rows of 1. The numbers 1, 2, 3, 4, 6, and 12 are all factors of 12 because they divide 12 exactly without any remainder.

Now let us learn about factors, multiples, and some special types of numbers!

What Is a Factor?

A factor is a number that divides another number exactly (with no remainder).

To find the factors of a number, think of all the pairs of numbers that multiply to give that number.

Think about it: 12 = 1 x 12, 12 = 2 x 6, 12 = 3 x 4. So the factors of 12 are: 1, 2, 3, 4, 6, 12.
Example
Finding All Factors -- Step by Step

Find all factors of 18:

18 = 1 x 18 → so 1 and 18 are factors

18 = 2 x 9 → so 2 and 9 are factors

18 = 3 x 6 → so 3 and 6 are factors

4 does not divide 18 exactly. 5 does not divide 18 exactly.

Factors of 18 = 1, 2, 3, 6, 9, 18

What Is a Multiple?

A multiple is the result you get when you multiply a number by 1, 2, 3, 4, 5, and so on.

Multiples are like the numbers in a multiplication table.

Example
First 10 Multiples

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

(4x1=4, 4x2=8, 4x3=12, 4x4=16, 4x5=20, 4x6=24, 4x7=28, 4x8=32, 4x9=36, 4x10=40)

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Common Factors and Common Multiples

Common factors are factors that two or more numbers share.

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18.

Common factors of 12 and 18: 1, 2, 3, 6 (these appear in both lists).

Common multiples are multiples that two or more numbers share.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36...

Common multiples of 3 and 4: 12, 24, 36...

Prime Numbers and Composite Numbers

A prime number has exactly 2 factors: 1 and itself. It cannot be divided evenly by any other number.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

A composite number has more than 2 factors. It can be divided by numbers other than 1 and itself.

Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Note: 1 is neither prime nor composite. It has only one factor (itself). The smallest prime number is 2.

More Examples

Example
Example: Indian Cricket Team

There are 15 players in a cricket squad. Can they be divided into equal groups? Factors of 15 = 1, 3, 5, 15. So they can form 3 groups of 5 or 5 groups of 3.

Example
Example: Sharing Sweets

Rani has 24 barfis. She wants to share them equally among her friends. She can share among 2 friends (12 each), 3 friends (8 each), 4 friends (6 each), 6 friends (4 each), 8 friends (3 each), or 12 friends (2 each). All these are factors of 24.

📝 Key Words

WordMeaning
FactorA number that divides another number exactly with no remainder
MultipleThe result of multiplying a number by 1, 2, 3, 4...
Common factorA factor shared by two or more numbers
Common multipleA multiple shared by two or more numbers
Prime numberA number with exactly 2 factors: 1 and itself
Composite numberA number with more than 2 factors
⭐ Key Points to Remember

✏️ Practice Questions

A. Find All the Factors
1. Factors of 16:
2. Factors of 20:
3. Factors of 30:
B. Write the First 10 Multiples
1. Multiples of 6:
2. Multiples of 9:
C. Fill in the Blanks
1. A number that divides another number exactly is called a .
2. The first five multiples of 8 are .
3. A prime number has exactly factors.
4. The smallest prime number is .
5. The number 1 is neither nor .
D. Multiple Choice Questions
1. Which of the following is a factor of 24?
(a) 5(b) 7(c) 8(d) 9
2. Which is a prime number?
(a) 9(b) 15(c) 17(d) 21
3. The common factors of 8 and 12 are:
(a) 1, 2, 4(b) 1, 2, 3(c) 1, 4, 8(d) 2, 4, 6
E. Short Answer Questions
1. Find the common factors of 12 and 16.
2. Write the first three common multiples of 4 and 6.
3. Is 27 a prime number or a composite number? Give a reason.
🎨 Think and Do -- Fun Activity

Prime Number Hunt: Look at the numbers from 1 to 30 below. Circle all the prime numbers and cross out all the composite numbers. Leave 1 unmarked.

12345678910
11121314151617181920
21222324252627282930

How many prime numbers did you find between 1 and 30?

Want to use this as a worksheet? Switch to the A4 printable view.

Learning Objectives
Let Us Begin!

Imagine you have 12 laddoos and you want to arrange them in equal rows. You can make 1 row of 12, 2 rows of 6, 3 rows of 4, 4 rows of 3, 6 rows of 2, or 12 rows of 1. The numbers 1, 2, 3, 4, 6, and 12 are all factors of 12 because they divide 12 exactly without any remainder.

Now let us learn about factors, multiples, and some special types of numbers!

What Is a Factor?

A factor is a number that divides another number exactly (with no remainder).

To find the factors of a number, think of all the pairs of numbers that multiply to give that number.

Think about it: 12 = 1 x 12, 12 = 2 x 6, 12 = 3 x 4. So the factors of 12 are: 1, 2, 3, 4, 6, 12.

Finding All Factors -- Step by Step

Find all factors of 18:

18 = 1 x 18 → so 1 and 18 are factors

18 = 2 x 9 → so 2 and 9 are factors

18 = 3 x 6 → so 3 and 6 are factors

4 does not divide 18 exactly. 5 does not divide 18 exactly.

Factors of 18 = 1, 2, 3, 6, 9, 18

What Is a Multiple?

A multiple is the result you get when you multiply a number by 1, 2, 3, 4, 5, and so on.

Multiples are like the numbers in a multiplication table.

First 10 Multiples

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

(4x1=4, 4x2=8, 4x3=12, 4x4=16, 4x5=20, 4x6=24, 4x7=28, 4x8=32, 4x9=36, 4x10=40)

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Common Factors and Common Multiples

Common factors are factors that two or more numbers share.

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18.

Common factors of 12 and 18: 1, 2, 3, 6 (these appear in both lists).

Common multiples are multiples that two or more numbers share.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36...

Common multiples of 3 and 4: 12, 24, 36...

Prime Numbers and Composite Numbers

A prime number has exactly 2 factors: 1 and itself. It cannot be divided evenly by any other number.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

A composite number has more than 2 factors. It can be divided by numbers other than 1 and itself.

Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Note: 1 is neither prime nor composite. It has only one factor (itself). The smallest prime number is 2.

Key Words and Meanings
WordMeaning
FactorA number that divides another number exactly with no remainder
MultipleThe result of multiplying a number by 1, 2, 3, 4...
Common factorA factor shared by two or more numbers
Common multipleA multiple shared by two or more numbers
Prime numberA number with exactly 2 factors: 1 and itself
Composite numberA number with more than 2 factors
Key Points to Remember
More Examples
Example: Indian Cricket Team

There are 15 players in a cricket squad. Can they be divided into equal groups? Factors of 15 = 1, 3, 5, 15. So they can form 3 groups of 5 or 5 groups of 3.

Example: Sharing Sweets

Rani has 24 barfis. She wants to share them equally among her friends. She can share among 2 friends (12 each), 3 friends (8 each), 4 friends (6 each), 6 friends (4 each), 8 friends (3 each), or 12 friends (2 each). All these are factors of 24.

Practice Questions

A. Find All the Factors

  1. Factors of 16:
  2. Factors of 20:
  3. Factors of 30:

B. Write the First 10 Multiples

  1. Multiples of 6:
  2. Multiples of 9:

C. Fill in the Blanks

  1. A number that divides another number exactly is called a .
  2. The first five multiples of 8 are .
  3. A prime number has exactly factors.
  4. The smallest prime number is .
  5. The number 1 is neither nor .

D. Multiple Choice Questions

  1. Which of the following is a factor of 24?
    (a) 5(b) 7(c) 8(d) 9
  2. Which is a prime number?
    (a) 9(b) 15(c) 17(d) 21
  3. The common factors of 8 and 12 are:
    (a) 1, 2, 4(b) 1, 2, 3(c) 1, 4, 8(d) 2, 4, 6

E. Short Answer Questions

  1. Find the common factors of 12 and 16.
  2. Write the first three common multiples of 4 and 6.
  3. Is 27 a prime number or a composite number? Give a reason.
Think and Do -- Fun Activity

Prime Number Hunt: Look at the numbers from 1 to 30 below. Circle all the prime numbers and cross out all the composite numbers. Leave 1 unmarked.

12345678910
11121314151617181920
21222324252627282930

How many prime numbers did you find between 1 and 30?