Generally, the Highest Common Factors are used to find the arithmetic operations of the fractions. There are different methods to find the Highest Common Factor. To find the HCF of Two Numbers by the division method, we write the small number in given numbers as a divisor and a large number as a dividend and then divide them. Divide the numbers until you get 0 in the last remainder.
Let us discuss the topic by considering Examples to find the highest common factor of two numbers by using the Division method. Before going into the topic let us discuss what HCF is exactly? HCF or Highest Common Factor is the greatest factor of any two or more numbers, which are common among them. Sometimes, it is also called the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD), or Highest Common Divisor (HCD).
Also, Read Some More Articles:
- Examples to find Highest Common Factor by using Prime Factorization Method
- To find Highest Common Factor by using Division Method
- To Find Lowest Common Multiple by using Division Method
- Examples to find Least Common Multiple of Two Numbers by using Division Method
HCF of Two numbers using Division Method Examples
Example 1:
Find the HCF of 18, 30 using the division method?
Solution:
Given the two numbers 18, and 30.
Now, we will find the factors of HCF using the division method.
In the division method, first, identify the smaller number and larger number. Because the small number is the divisor and the large number is a dividend.
So, the divisor is 18 and the dividend is 30. Let us see the below figure how to perform the division operation,
So, 6 is exactly the divided prime factors of 18, and 30.
Therefore, the HCF of the two given numbers is 6.
Example 2:
Find the HCF of 852, and 1065. Using the division method.
Solution:
As given in the question, the values are 852, 1065
Now, we will find the Highest Common Factor value.
The below figure explains the division operation,
Hence, 213 is the HCF of 852, and 1065.
Example 3:
Find the HCF of 42, 62 using the division method and leaving 2 as the remainder?
Solution:
Given as the number divides 62 and leaves 2 as the remainder.
So, the number divides 62 – 2 = 60 exactly.
The number divides 42 and leaves 2 because of the remainder.
So, the number divides 40 – 2 = 40 exactly.
Now, we’ve to find the HCF(40, 60)
Hence, 20 is the Highest Common Factor of 40, and 60.
Example 4:
What is the HCF of 180, 270 using the division method?
Solution:
Given the values are 180, 270.
Now, find the factors using the division method. In the division method, first, take the small number as the divisor and the larger number as a dividend. Like as shown within the below figure,
Now, Divide the given number to get the remainder as 90. Next, again divide 180 by 90, we get the remainder as 0.
Then, we write the prime factors, the left-hand side dividend numbers are factors.
The factors are 180, and 90. But 90 is exactly divided and the remainder is 0.
Therefore, the HCF of 180, and 270 is 15.
Example 5:
Find the HCF of two given numbers using the division method. The numbers 30, 42?
Solution:
Given the value is 30, 42
Using the division Method, we are going to find the value.
First, divide 30 and 42. So, 30 will be the divisor and 42 will be the dividend.
Now the remainder will become 12, 12 is the new divisor and 30 will become the new dividend. We get the remainder value as 6.
Proceed with this process the 6 will be divisor and 12 will be dividend then the remainder is zero and the last divisor will be the HCF of the given number.
The above figure shows the entire process of the division method.
So, 6 will be exactly divided and the remainder is 0, so the process ends.
Hence, the HCF of the given two numbers is 6.
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FAQ’s on HCF of Two Numbers
1. What are the steps to find the HCF of two numbers of the Division Method?
The following are the steps for finding the HCF of two given numbers using the division method,
Step 1: Initially, Divide the largest number by the smallest number.
Step 2: Next, take the divisor as new a dividend and remainder as the new divisor, it means to divide the initial divisor by the first remainder.
Step 3: Proceed with till the remainder is zero and thus the last divisor goes to be the HCF of the given numbers.
2. What is the Highest Common Factor?
The Highest Common Factor of two or more numbers is nothing but the highest number among all the common factors of given numbers.
3. What is the HCF of 120 and 100?
Given,
Now, allow us to find the HCF by using the division method.
Divide 120 by 100.
120/100 → 1 and remainder is 20
Now, divide the first divisor 100 by the first remainder of 20.
100/20 → 5 and remainder is 0.
Therefore, 20 is that the HCF of 120 and 100.
4. What is the HCF Formula?
HCF of a given number is always divided by its L.C.M. To find the greatest number which will exactly divide x and y. Required number = HCF of x, y. To find the largest number that will divide x and y leaving remainders as a, b, and c respectively.
5. What are the methods used for finding the Highest Common Factor?
For finding the Highest Common Factor of two or more numbers, we have three methods,
1. Division Method
2. Factorization Method
3. Prime Factorization Method.