HCF of 36, 48, 60, 108 using Euclid's algorithm
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Want to know how to use Euclid’s algorithm to find the HCF of 36, 48, 60, 108 ? Well, you have come to the right place. In this article, you will be learning about Euclid’s algorithm and how to use it to calculate the HCF with ease.
Take the help of the HCF Calculator using the Euclid Division Algorithm which finds HCF of 36, 48, 60, 108 using Euclid's algorithm i.e 12 quickly.
Detailed Method to Find the HCF of 36,48,60,108 using Euclid's algorithm
Euclid’s algorithm is written as a = bq + r. This is known as the division lemma. The variable r varies according to 0 ≤ r ≤ b. We can use this to figure out the HCF of 36,48,60,108. This is how to do it.
Step 1: The first step is to use the division lemma with 48 and 36 because 48 is greater than 36
48 = 36 x 1 + 12
Step 2: Here, the reminder 36 is not 0, we must use division lemma to 12 and 36, to get
36 = 12 x 3 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 12.Therefore, the HCF of 36 and 48 is equal to 12
Notice that 12 = HCF(36,12) = HCF(48,36) .
Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next
Step 1: The first step is to use the division lemma with 60 and 12 because 60 is greater than 12
60 = 12 x 5 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 12.Therefore, the HCF of 12 and 60 is equal to 12
Notice that 12 = HCF(60,12) .
Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next
Step 1: The first step is to use the division lemma with 108 and 12 because 108 is greater than 12
108 = 12 x 9 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 12.Therefore, the HCF of 12 and 108 is equal to 12
Notice that 12 = HCF(108,12) .
Result
Hence, the HCF of 36, 48, 60, 108 is equal to 12.
FAQ on HCF of 36, 48, 60, 108 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid’s algorithm is represented as a = bq + r, and 0 ≤ r ≤ b..
2. How do you find HCF using Euclid's algorithm ?
Answer: Apply the division lemma to the numbers, and keep going until the remainder is zero. Once it becomes zero, the divisor will be your HCF.
3. What is the HCF of 36, 48, 60, 108?
Answer: The HCF of 36, 48, 60, 108 is 12.