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**Factors and Multiples**

## Highest Common Factor for Class 5 Math

The full form of HCF is the highest common factor. Here students will learn the HCF definition and HCF meaning.

In this learning concept, the students can

- Representation of the HCF by prime factorization method and HCF by division method.
- Interpret how to find the HCF of two numbers.
- Application of HCF question word problem.

Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable worksheets given at the page’s end.

Download the HCF question worksheet for class 5 and check the solutions for the concept of the HCF question provided in PDF format.

## What Is HCF?

- The factors of a number are those numbers that are exactly divisible by the given number.
- The common factor of the number are the factors that are common to the two or more numbers.

### Example:

- The factor of the numbers 8 and 12 are:
- The common factors of 8 and 12 are the list of the numbers which is common in the factors of 8 and 12.
- Therefore, the
**common factors**of 8 and 12 are:

Factor of 8 = 1, 2, 4, and 8.

Factor of 12 = 1, 2, 3, 4, 6, and 12.

1, 2, and 4.

Highest Common Factor

- The highest common factor is the largest of the common factors.
- It is also known as the
**greatest common divisor**. - It is also written as HCF or GCD

Methods to Find the HCF

- Common factors method
- Prime factorization method
- Division method

## How to Find the HCF of Two Numbers?

- Write the factors of the numbers.
- List the common factors of the numbers.
- Choose the largest common factor.

### Example:

Find the highest common factor of 8 and 12.

Solution:

Factor of 8 = 1, 2, 4, and 8.

The factors of 12: 1, 2, 3, 4, 6, and 12.

The common factors of 8 and 12 are: 1, 2, and 4.

The largest common factor of 8 and 12 is 4. Therefore, HCF or the highest common factor of 8 and 12 is 4.

## HCF by Prime Factorization Method

- Write the prime factorization of each number.
- Circle the common prime factors.
- Multiply the common prime factors.
- The obtained product is equal to the HCF of the numbers.

### Example:

Find the HCF of 12 and 16.

Solution:

Step 1:

Find the prime factorization of 12.

Step 2:

Find the prime factorization of 16.

Step 3:

Encircle the common prime factors.

Step 4:

Multiply the common prime factors.

2 × 2 = 4

Therefore, the highest common factor or HCF of 12 and 16 is 4.

## HCF by Division Method

- Divide the larger number by the smaller number.
- Divide the divisor by the remainder.
- Repeat the process of dividing the divisor by the remainder until you get 0 as the remainder.
- The last obtained divisor is the HCF of the numbers.

### Example:

Find the HCF of 20 and 36.

Solution:

- Divide 36 by 20.
- Divide 20 by 16.
- Divide 16 by 4.

Since the last remainder is 0 therefore, the last divisor is equal to the HCF of 20 and 36.

HCF = 4

## HCF Questions Word Problem

### Example:

There are 12 girls and 8 boys in the class. The teacher wants to place them in equal rows. Find the greatest number of students who can be in each row.

Solution:

Number of girls = 12

Number of boys = 8

Obtain the greatest common factor of 12 and 8.

HCF = 2 × 2

= 4

Therefore, the greatest number of students in each row is 4.

Fun Facts:

Did you know?

An English Mathematician, William Oughtred invented the symbol “×” for multiplication.