how to find HCF using Graph Paper(METHOD)
Answers
Answer:
The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. It is also called the Greatest Common Measure(GCM) and Greatest Common Divisor(GCD). HCM and LCM are two different methods, whereas LCM or Least Common Multiple is used to find the smallest common multiple of any two or more numbers.
Example: The Highest common factor of 60 and 75 is 15 because 15 is the largest number which can divide both 60 and 75 exactly.
We can find the HCF of any given numbers by using two methods:
by prime factorization method
by division method
Let us discuss these two methods one by one in this article.
Step-by-step explanation:
HCF By Prime Factorization Method
Follow the below-given steps to find the hcf of numbers using prime factorisation method.
Step 1: Write each number as a product of its prime factors. This method is called here prime factorization.
Step 2: Now list the common factors of both the numbers
Step 3: The product of all common prime factors is the HCF ( use the lower power of each common factor)
Let us understand with the help of examples.
Example 1: Evaluate the HCF of 60 and 75.
Solution:
Write each number as a product of its prime factors.
22 x 3 x 5 = 60
3 x 52 = 75
The product of all common prime factors is the HCF.
The common prime factors in this example are 3 & 5.
The lowest power of 3 is 3 and 5 is 5.
So, HCF = 3 x 5 = 15
Example 2: Find the HCF of 36, 24 and 12.
Solution:
Write each number as a product of its prime factors.
22 x 32 = 36
23 x 3 = 24
22 x 3 = 12
The product of all common prime factors is the HCF ( use the lowest power of each common factor)
The common prime factors in this example are 2 & 3.
The lowest power of 2 is 22 and 3 is 3.
So, HCF = 22 x 3 = 12
Example 3: Find the HCF of 36, 27 and 80.
Solution:
Write each number as a product of its prime factors.
22 x 32 = 36
33 = 27
24 x 5 = 80
The product of all common prime factors is the HCF
The common prime factors in this example are none.
So, HCF is 1.
HCF By Division Method
You have understood by now the method of finding the highest common factor using prime factorization. Now let us learn here to find HCF using division method. Basically division method is nothing but dividing the given numbers, simultaneously, to get the common factors between them. Follow the steps mentioned below to solve problems of hcf.
Step 1: Write the given numbers horizontally, in a sequence, by separating it with commas.
Step 2: Find the smallest prime number which can divide the given number. It should exactly divide the given numbers. (Write on the left side).
Step 3: Now write the quotients.
Step 4: Repeat the process, until you reach the stage, where there is no coprime number left.
Step 5: We will get the common prime factors as the factors in the left-hand side divides all the numbers exactly. The product of these common prime factors is the HCF of the given numbers.
Let us understand the above-mentioned steps to find the HCF by division method with the help of examples.
Problem 1: Evaluate the HCF of 30 and 75
HCF Example1
As we can note that the mentioned prime factors, on the left side, divide all the numbers exactly. So, they all are common prime factors. We have no common prime factor for the numbers remained at the bottom.
So, HCF = 3 × 5 = 15.
Example 2: Find out HCF of 36, and 24
highest common factors Example
HCF = 2 × 2 × 3 = 12.
Example 3: Find out HCF of 36, 12, 24 and 48.
HCF by division method
HCF = 2 × 2 × 3 = 12.
HCF by Shortcut method
Steps to find the HCF of any given numbers.
Step 1: Divide larger number by smaller number first, such as;
Larger Number/Smaller Number
Step 2: Divide the divisor of step 1 by the remainder left.
Divisor of step 1/Remainder
Step 3: Again divide the divisor of step 2 by the remainder.
Divisor of step 2/Remainder
Step 4: Repeat the process until the remainder is zero.
Step 5: The divisor of the last step is the HCF.
How to find the HCF of 3 numbers
1) Calculate the HCF of 2 numbers.
2) Then Find the HCF of 3rd number and the HCF found in step 1.
3) The HCF you got in step 2 will be the HCF of the 3 numbers.
The above steps can also be used to find the HCF of more than 3 numbers.
HCF Examples
Here is a few more example to find the highest common factors.
Example 1: Find out HCF of 30 and 45.
Finding HCF by Shortcut method
So, the HCF of 30 and 45 is 15.
Example 2: Find out HCF of 12 and 36.
HCF by shortcut method
So, HCF of 12 and 36 = 12
Example 3: Find out HCF of 9, 27, and 30
Take any two numbers and find out their HCF first. Say, let’s find out HCF of 9 and 27 initially.
highest common factors by shortcut method
So, HCF of 9 and 27 = 9
HCF of 9 ,27, 30
= HCF of [(HCF of 9, 27) and 30
= HCF of [9 and 30]
Shortcut method for hcf
Hence, HCF of 9 ,27, 30 = 3
Example 4: Find out HCF of 5 and 7
HCF Calculation
Hence, HCF of 5 and 7 = 1