 # Properties of H.C.F – Formulas & Tricks | Highest Common Factor Properties with Examples

The greatest common factor for two or more natural numbers is known as HCF. The properties of HCF are given in the below section. Also learn the relationship between HCF and LCM from this page. For better understanding, we have provided various questions with a brief explanation here. So, the students who are lagging the Highest Common Factors concept practice the problems given in this article and enhance their math skills.

## What is meant by H.C.F?

HCF is nothing but Highest or Greatest Common Factor. H.C.F is found by multiplying factors which is appeared in both the numbers. There are few methods to find the HCF of two or more numbers. Division method, prime factorization method, and factorization methods are known to find the Highest Common Factors or Greatest Common Factors of the given numbers. The highest factors among both the given numbers are considered as H.C.F
Example: Find the HCF of 21 and 42.
Solution:
Given two numbers 21 and 42.
First, find the factors of 21 and 42.
The factors of 21 are 3, 7, 21
The factors of 42 are 2, 6, 7, 14, 21 and 42.
The common factors of 21 and 42 are 7 and 21.
The highest among both is 21.
Thus the HCF of 21 and 42 is 21.

### Properties of HCF | Highest Common Factor Properties

Property 1.
HCF of any two or more numbers is never greater than any of the given numbers.
Example: HCF of 2 and 4 is 2.
Here one number is 2 itself and another number 4 is greater than HCF i.e, 2
Property 2.
If one number is a factor of the other numbers, their HCF will be that smallest number.
Example: HCF of 8 and 16 is 8.
Property 3.
The H.C.F. of the numbers is the product of the co-prime factors.

Example 1.
What is the Highest Common Factor of 30 and 36?
Solution:
First, we have to find the factors of 30 and 36.
30 = 1 × 30
= 2 × 15
= 3 × 10
= 5 × 6
= 6 × 5
= 10 × 3
= 15 × 2
= 30 × 1
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
Now identify the common factors of 30 and 36 – 1, 2, 3, 6.
The highest common factor is 6.

Example 2.
What is the HCF of 24 and 96?
Solution:
First, we have to find the factors of 24 and 96.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.
Now identify the common factors of 24 and 96 – 1, 2, 3, 4, 6, 8, 12, 24.
Thus the HCF of 24 and 96 is 24.

Example 3.
What is the HCF of 14 and 28?
Solution:
First, we have to find the factors of 14 and 28.
Prime factorization of 14 is 2 × 7
Prime factorization of 28 is 2 × 2 × 7
The common factors are 2 × 7
Thus the HCF of the two numbers 14 and 28 is 14.

Example 4.
What is the HCF of 21 and 35?
Solution:
First, we have to find the prime factors of two numbers 21 and 35.
After we will calculate the factors of 21 and 35 and find the highest common factor number.
Prime factorization of 21 is 3 × 7
Prime factorization of 35 is 5 × 7
The factors of 21 are 1, 3, 7, 21
The factors of 35 are 1, 5, 7, 35
The common factors of 21 and 35 are 7.
Thus the Highest Common Factor of 21 and 35 is 7.

Example 5.
What is the HCF of the two numbers 51 and 68?
Solution:
We will first find the prime factorization of 51 and 68.
After we will calculate the factors of 51 and 68 and find the highest common factor number.
Prime factorization of 51 = 3 × 17
Prime factorization of 68 = 2 × 2 × 17
The factors of 51 are 1, 3, 17, 51
The factors of 68 are 1, 2, 17, 68
The common factors are 1, 17
The highest common factor of 51 and 68 is 17.

### FAQs on Highest Common Factors

1. How do you find the HCF of the numbers?

There are many ways to find the highest common factor of the given numbers.
1. HCF by listing out the common factors
2. HCF by prime factorization
3. HCF by division method

2. What is the formula of HCF?

HCF = HCF of Numerators/LCM of Denominators

3. Write an Example of HCF?

Example: Find the H.C.F of 10 and 25.
Solution:
Find the factors of 10 and 25.
Factors of 10 are 1, 2, 5, and 10.
Factors of 25 are 1, 5, 5, 25.
The common factors of 10 and 25 are 1, 5
The HCF of 10 and 20 is 5.

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