HCF of 210, 308 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 210, 308 ? 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 210, 308 using Euclid's algorithm i.e 14 quickly.
Detailed Method to Find the HCF of 210,308 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 210,308. This is how to do it.
Step 1: The first step is to use the division lemma with 308 and 210 because 308 is greater than 210
308 = 210 x 1 + 98
Step 2: Here, the reminder 210 is not 0, we must use division lemma to 98 and 210, to get
210 = 98 x 2 + 14
Step 3: We consider the new divisor 98 and the new remainder 14, and apply the division lemma to get
98 = 14 x 7 + 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 14.Therefore, the HCF of 210 and 308 is equal to 14
Notice that 14 = HCF(98,14) = HCF(210,98) = HCF(308,210) .
Result
Hence, the HCF of 210, 308 is equal to 14.
FAQ on HCF of 210, 308 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 210, 308?
Answer: The HCF of 210, 308 is 14.