HCF of 108, 72 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 108, 72 ? 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 108, 72 using Euclid's algorithm i.e 36 quickly.
Detailed Method to Find the HCF of 108,72 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 108,72. This is how to do it.
Step 1: The first step is to use the division lemma with 108 and 72 because 108 is greater than 72
108 = 72 x 1 + 36
Step 2: Here, the reminder 72 is not 0, we must use division lemma to 36 and 72, to get
72 = 36 x 2 + 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 36.Therefore, the HCF of 108 and 72 is equal to 36
Notice that 36 = HCF(72,36) = HCF(108,72) .
Result
Hence, the HCF of 108, 72 is equal to 36.
FAQ on HCF of 108, 72 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 108, 72?
Answer: The HCF of 108, 72 is 36.