HCF of 84, 396 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 84, 396 ? 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 84, 396 using Euclid's algorithm i.e 12 quickly.
Detailed Method to Find the HCF of 84,396 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 84,396. This is how to do it.
Step 1: The first step is to use the division lemma with 396 and 84 because 396 is greater than 84
396 = 84 x 4 + 60
Step 2: Here, the reminder 84 is not 0, we must use division lemma to 60 and 84, to get
84 = 60 x 1 + 24
Step 3: We consider the new divisor 60 and the new remainder 24, and apply the division lemma to get
60 = 24 x 2 + 12
We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get
24 = 12 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 12.Therefore, the HCF of 84 and 396 is equal to 12
Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) = HCF(396,84) .
Result
Hence, the HCF of 84, 396 is equal to 12.
FAQ on HCF of 84, 396 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 84, 396?
Answer: The HCF of 84, 396 is 12.