## Introduction to HCF

What if you need to find the maximum common dimension for any two clothes having different sizes?. Here we use HCF as the most common and most efficient way.

The HCF of two numbers is the biggest number that can divide both evenly.

HCF can be evaluated for two or more numbers.

The greatest common factor of any two numbers will divide it completely or equally the given numbers.

For example – the HCF of 9 and 15 is 3. Because 3 is the largest number it can divide 9 and 15 exactly.

HCF

### Methods To HCF

There are two methods of finding HCF.

Division method

### Prime Factorization Method

Prime factorization is the simple process of finding the prime numbers when multiplied together to get the original number.

To understand it better let’s solve one example , Are you Ready!

Let’s start

Find the common factors of 30 and 45.

Find HCF of 30 and 45,

First, we will get each number as a product of prime factors.

So, for 30 = 2 x 3 x 5

And for 45 = 3 x 3 x 5

The product of all common prime factors is the HCF

2 x 3 x 5

3 x 3 x 5

The blue colour is common in both.

So the HCF = 5 X 3 = 15.

HCF of 30 and 45

### Division Method

In the division method, we will divide the largest number by the smallest number until we get the remainder as 0.

To understand it better, let's solve an example.

We will use same question, we have used for prime factorization method

Let’s Start

Find HCF of 30 and 45,

HCF of 30 and 45

As we can see in the image, the greatest number 45 is divided by the smallest number 30. After diving, we get a remainder of 15. Now we have 15 and 30, we will repeat the method. We will divide the largest number by the smallest here. The largest number is 30 and the smallest number is 15. We will divide 30 by 15 and we get the remainder as 0. Hence, the HCF of 30 and 45 is 15.

## HCF Solved Examples

Question 1: find HCF of 30 and 50

Solution: 30 = 2 x 3 x 5

50= 2 x 5 x 5

HCF = 2 x 5 =10.

Question 2: Find the HCF of 30 and 60 by both methods.

Solution:

HCF of 30 and 60 by factorization method

30 = 2 x 3 x 5

60 = 2 x 2 x 3 x 5

So here 2,3 and 5 are the common factors in it.

HCF = 2 x 3 x 5 = 30

HCF = 30

HCF of 30 and 60 by division method

Ans:

HCF of 30 and 60

As after dividing the largest number by smallest we are getting 0 as remainder.

So the HCF will be 30

HCF = 30.

## HCF Properties

Let’s see some interesting properties of HCF –

The HCF of two numbers cannot be greater than any of them.

If one number is the factor of another number, the smaller number will be the HCF in this case.

Eg:- HCF of 10 and 5 will be 5 only.

The HCF of two numbers is the product of common prime factors.

The HCF of co-prime numbers will always be equal to 1. (same goes for prime numbers also.

## HCF Math Question

Question 1: What is the greatest number which can divide 44, 70, and 82?

Solution: By prime factorization method;

44 = 2 x 2 x 11

70 = 2 x 5 x 7

82 = 2 x 41

So here 2 is the only common factor for 44, 70 and 82

HCF = 2.

Question 2: Find the HCF of 20 , 50

Solution: In the fraction, we have to do the HCF of all the numerators and LCM of all the denominators.

So we have to find HCF of 20,50

And LCM of 20 , 50

Let’s find HCF first,

20= 2 x 2 x 5

50 = 2 x 5 x 5

2 and 5 the only common factor here,

So HCF = 2 x 5 = 10

**Summary**

In this article, we got to know about HCF. It can be found for 2 or more numbers. We also learnt that there are 2 methods to find HCF. We can find HCF either by prime factorization or by division method. We got to know about its properties and real-life use of it. And now we can use this knowledge to solve various types of HCF-related problems.

## FAQs on Highest Common Factor of 30

1. What is the importance of using the highest common factors?

This method can be especially beneficial when finding prime factors or inverses because it makes it much easier to identify all prime factors and reciprocals on one line (in contrast with how reversing an equation plays out). H.C.F is mainly used in mathematical problems to split things into smaller sections.

2. Expand GCF?

Greatest Common Factor

3. What is the HCF of co-prime numbers?

CO-prime numbers are those numbers that have 1 as their common factor. These are not necessarily prime numbers.