How to find HCF of 852, 1491, 2343 using Euclid's Algorithm?

For arbitrary numbers 852, 1491, 2343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

How to find HCF of 852, 1491, 2343 using Euclid's Algorithm?

For arbitrary numbers 852, 1491, 2343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

HCF of 852, 1491, 2343 using Euclid's algorithm

Q: What is the Euclid division algorithm?

Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

Q: what is the HCF of 852, 1491, 2343?

HCF of 852, 1491, 2343 is 213 the largest number that divides all the numbers leaving a remainder zero.

Created By : Jatin Gogia
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023

Want to know how to use Euclid’s algorithm to find the HCF of 852, 1491, 2343 ? 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 852, 1491, 2343 using Euclid's algorithm i.e 213 quickly.

Detailed Method to Find the HCF of 852,1491,2343 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 852,1491,2343. This is how to do it.

Step 1: The first step is to use the division lemma with 1491 and 852 because 1491 is greater than 852

1491 = 852 x 1 + 639

Step 2: Here, the reminder 852 is not 0, we must use division lemma to 639 and 852, to get

852 = 639 x 1 + 213

Step 3: We consider the new divisor 639 and the new remainder 213, and apply the division lemma to get

639 = 213 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 213.Therefore, the HCF of 852 and 1491 is equal to 213

Notice that 213 = HCF(639,213) = HCF(852,639) = HCF(1491,852) .

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 2343 and 213 because 2343 is greater than 213

2343 = 213 x 11 + 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 213.Therefore, the HCF of 213 and 2343 is equal to 213

Notice that 213 = HCF(2343,213) .

Result

Hence, the HCF of 852, 1491, 2343 is equal to 213.

FAQ on HCF of 852, 1491, 2343 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 852, 1491, 2343?

Answer: The HCF of 852, 1491, 2343 is 213.