HCF of 60, 468 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 60, 468 ? 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 60, 468 using Euclid's algorithm i.e 12 quickly.
Detailed Method to Find the HCF of 60,468 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 60,468. This is how to do it.
Step 1: The first step is to use the division lemma with 468 and 60 because 468 is greater than 60
468 = 60 x 7 + 48
Step 2: Here, the reminder 60 is not 0, we must use division lemma to 48 and 60, to get
60 = 48 x 1 + 12
Step 3: We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get
48 = 12 x 4 + 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 60 and 468 is equal to 12
Notice that 12 = HCF(48,12) = HCF(60,48) = HCF(468,60) .
Result
Hence, the HCF of 60, 468 is equal to 12.
FAQ on HCF of 60, 468 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 60, 468?
Answer: The HCF of 60, 468 is 12.