HCF for Class 5: Step-by-Step Guide for Kids with Easy Examples

The Highest Common Factor (HCF) is an important maths concept that helps Class 5 students to solve problems in a simple way. In this article students will learn that the Highest Common Factor (HCF) is the largest number that divides two or more numbers exactly without a remainder.

Table of Contents

• What is HCF?
• Formula for HCF
• Methods to Find HCF
• Solved Examples on HCF for Class 5
• Practice Questions on HCF for Class 5
• HCF Worksheet for Class 5

What is HCF?

HCF stands for Highest Common Factor. It is also called the Greatest Common Divisor or GCD. The HCF of two or more numbers is the largest number that divides all of them without leaving any remainder. The highest common factor is the largest of all the common factors. In the example above, the common factors of 12 and 18 are 1, 2, 3, and 6. The highest common factor is 6. This is the largest number that divides both 12 and 18.

We can write this as HCF of 12 and 18 is 6, or we can write it as HCF (12, 18) = 6.

Formula for HCF

There is no specific formula for HCF like we have in algebra. However, we can use different methods to find the HCF. These methods help us calculate the HCF of two or more numbers systematically.

The relationship between HCF and LCM is given by the formula:

HCF × LCM = Product of the two numbers

In mathematical form:

HCF (a, b) × LCM (a, b) = a × b

Here, a and b are any two numbers, HCF is the Highest Common Factor, and LCM is the Least Common Multiple.

Methods to Find HCF

There are different methods to find the HCF of two or more numbers. Let us learn each method in detail.

METHOD 1: LISTING FACTORS METHOD

This is the simplest method to find HCF. In this method, we list all the factors of each number and then find the common factors. The largest common factor is the HCF.

Step 1: List all the factors of the first number.

Step 2: List all the factors of the second number.

Step 3: Identify the common factors from both lists.

Step 4: Find the largest common factor. This is the HCF.

EXAMPLE 1: Find HCF of 20 and 30.

Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Common factors: 1, 2, 5, 10

Highest common factor: 10

Therefore, HCF (20, 30) = 10

EXAMPLE 2: Find HCF of 15 and 25.

Factors of 15: 1, 3, 5, 15

Factors of 25: 1, 5, 25

Common factors: 1, 5

Highest common factor: 5

Therefore, HCF (15, 25) = 5

METHOD 2: PRIME FACTORIZATION METHOD

In this method, we find the prime factors of each number. Then we multiply the common prime factors to get the HCF.

Step 1: Find the prime factorization of the first number.

Step 2: Find the prime factorization of the second number.

Step 3: Identify the prime factors that are common to both numbers.

Step 4: Multiply all the common prime factors. This is the HCF.

If a prime factor appears more than once, we take only the one with the smallest power.

EXAMPLE 1:

Find HCF of 24 and 36.

Prime factorization of 24: 2 × 2 × 2 × 3 = 2³ × 3

Prime factorization of 36: 2 × 2 × 3 × 3 = 2² × 3²

Common prime factors: 2 and 3

We take 2² (the smaller power) and 3¹ (the smaller power)

HCF = 2² × 3 = 4 × 3 = 12

Therefore, HCF (24, 36) = 12

EXAMPLE 2:

Find HCF of 18 and 24.

Prime factorization of 18: 2 × 3 × 3 = 2 × 3²

Prime factorization of 24: 2 × 2 × 2 × 3 = 2³ × 3

Common prime factors: 2 and 3

We take 2¹ (the smaller power) and 3¹ (the smaller power)

HCF = 2 × 3 = 6

Therefore, HCF (18, 24) = 6

METHOD 3: DIVISION METHOD (LONG DIVISION METHOD)

In this method, we use the long division method to find the HCF. This method is also called Euclid's algorithm.

Step 1: Take the larger number as the dividend and the smaller number as the divisor.

Step 2: Divide the larger number by the smaller number.

Step 3: The remainder becomes the new divisor and the previous divisor becomes the new dividend.

Step 4: Repeat this process until the remainder is zero.

Step 5: The last divisor is the HCF.

EXAMPLE : Find HCF of 15 and 20 using Division Method

Step 1: 20 ÷ 15 = 1 remainder 5
Step 2: 15 ÷ 5 = 3 remainder 0

Since remainder is 0, HCF = 5                          

METHOD 4: COMMON DIVISION METHOD

In this method, we divide both numbers by a common factor and continue until no more common factors exist.

Step 1: Find a number that divides both given numbers.

Step 2: Divide both numbers by this common number.

Step 3: Repeat this process with the quotients until we cannot find a common factor.

Step 4: Multiply all the common factors. This is the HCF.

EXAMPLE: Find HCF of 24 and 36.

        24    36
÷ 2     12    18
÷ 2      6     9
÷ 3      2     3

No more common factors.
HCF = 2 × 2 × 3 = 12

Now 2 and 3 have no common factor other than 1.

HCF = 2 × 2 × 3 = 12

Therefore, HCF (24, 36) = 12

Solved Examples on HCF for Class 5

1: FINDING HCF USING LISTING FACTORS METHOD

Problem: Find the HCF of 12 and 18.

Solution:

Factors of 12: 1, 2, 3, 4, 6, 12

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

Common factors: 1, 2, 3, 6

The highest common factor is 6.

Answer: HCF (12, 18) = 6

2: FINDING HCF USING PRIME FACTORIZATION

Problem: Find the HCF of 20 and 30.

Solution:

Prime factorization of 20: 2 × 2 × 5 = 2² × 5

Prime factorization of 30: 2 × 3 × 5

Common prime factors: 2 and 5

HCF = 2 × 5 = 10

Answer: HCF (20, 30) = 10

3: FINDING HCF USING DIVISION METHOD

Problem: Find the HCF of 48 and 64.

Solution:

Using the long division method:

• 64 ÷ 48 = 1 remainder 16
• 48 ÷ 16 = 3 remainder 0

The HCF is 16.

Answer: HCF (48, 64) = 16

4: FINDING HCF OF THREE NUMBERS

Problem: Find the HCF of 12, 18, and 24.

Solution:

First, find the HCF of 12 and 18.

Factors of 12: 1, 2, 3, 4, 6, 12

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

HCF (12, 18) = 6

Now find the HCF of 6 and 24.

Factors of 6: 1, 2, 3, 6

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

HCF (6, 24) = 6

Answer: HCF (12, 18, 24) = 6

5: WORD PROBLEM ON HCF

Problem: Ravi has 24 red marbles and 36 blue marbles. He wants to divide them into equal groups such that each group has the same number of red marbles and the same number of blue marbles. What is the maximum number of groups he can make?

Solution:

To find the maximum number of groups, we need to find the HCF of 24 and 36.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors: 1, 2, 3, 4, 6, 12

HCF (24, 36) = 12

Answer: Ravi can make 12 groups. Each group will have 2 red marbles and 3 blue marbles.

6: FINDING HCF WITH LARGER NUMBERS

Problem: Find the HCF of 56 and 84.

Solution:

Prime factorization of 56: 2 × 2 × 2 × 7 = 2³ × 7

Prime factorization of 84: 2 × 2 × 3 × 7 = 2² × 3 × 7

Common prime factors: 2 and 7

Taking the smallest powers: 2² and 7¹

HCF = 2² × 7 = 4 × 7 = 28

Answer: HCF (56, 84) = 28

7: WORD PROBLEM ON GROUPING

Problem: A school has 30 boys and 45 girls. They want to form groups where each group has an equal number of boys and an equal number of girls. What is the maximum number of groups that can be formed?

Solution:

To find the maximum number of groups, we need to find the HCF of 30 and 45.

Prime factorization of 30: 2 × 3 × 5

Prime factorization of 45: 3 × 3 × 5 = 3² × 5

Common prime factors: 3 and 5

HCF = 3 × 5 = 15

Answer: The maximum number of groups is 15. Each group will have 2 boys and 3 girls.

8: FINDING HCF USING COMMON DIVISION

Problem: Find the HCF of 40 and 60 using the common division method.

Solution:

        40    60
÷ 2     20    30
÷ 2     10    15
÷ 5      2     3

Now 2 and 3 have no common factor other than 1.

HCF = 2 × 2 × 5 = 20

Answer: HCF (40, 60) = 20

9: WORD PROBLEM ON CUTTING PIECES

Problem: Priya has two ribbons, one 24 centimeters long and another 36 centimeters long. She wants to cut them into equal pieces without any leftover. What is the maximum length of each piece?

Solution:

To find the maximum length of each piece, we need to find the HCF of 24 and 36.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors: 1, 2, 3, 4, 6, 12

HCF (24, 36) = 12

Answer: The maximum length of each piece is 12 centimeters. She can cut 2 pieces from the first ribbon and 3 pieces from the second ribbon.

10: FINDING HCF AND VERIFYING WITH FORMULA

Problem: Find the HCF of 12 and 18. Also verify using the HCF and LCM formula.

Solution:

Factors of 12: 1, 2, 3, 4, 6, 12

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

Common factors: 1, 2, 3, 6

HCF (12, 18) = 6

To verify using the formula: HCF × LCM = Product of the two numbers

Multiples of 12: 12, 24, 36, 48, 60...

Multiples of 18: 18, 36, 54, 72...

LCM (12, 18) = 36

HCF × LCM = 6 × 36 = 216

Product of numbers = 12 × 18 = 216

The formula is verified: 216 = 216

Answer: HCF (12, 18) = 6, and the formula HCF × LCM = Product is verified.

Practice Questions on HCF for Class 5

1: BASIC HCF - LISTING FACTORS

Find the HCF of 8 and 12.

2: HCF OF TWO NUMBERS

Find the HCF of 15 and 25.

3: HCF OF LARGER NUMBERS

Find the HCF of 36 and 48.

4: HCF USING DIVISION METHOD

Find the HCF of 28 and 42.

5: HCF OF THREE NUMBERS

Find the HCF of 10, 15, and 20.

6: WORD PROBLEM - MAKING GROUPS

Sahil has 18 pencils and 24 erasers. He wants to pack them into boxes such that each box has equal number of pencils and erasers. What is the maximum number of boxes he can make?

7: HCF OF CONSECUTIVE NUMBERS

Find the HCF of 20 and 30.

8: WORD PROBLEM - CUTTING RIBBONS

Meera has two pieces of cloth measuring 32 meters and 48 meters. She wants to cut them into equal pieces without any waste. What is the maximum length of each piece?

9: HCF WITH PRIME NUMBERS

Find the HCF of 17 and 19.

10: HCF OF EQUAL NUMBERS

Find the HCF of 16 and 16.

HCF Worksheet for Class 5