How to find HCF of 52, 65, 91 using Euclid's Algorithm?

For arbitrary numbers 52, 65, 91 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 52, 65, 91 using Euclid's Algorithm?

For arbitrary numbers 52, 65, 91 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 52, 65, 91 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 52, 65, 91?

HCF of 52, 65, 91 is 13 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 52, 65, 91 ? 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 52, 65, 91 using Euclid's algorithm i.e 13 quickly.

Detailed Method to Find the HCF of 52,65,91 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 52,65,91. This is how to do it.

Step 1: The first step is to use the division lemma with 65 and 52 because 65 is greater than 52

65 = 52 x 1 + 13

Step 2: Here, the reminder 52 is not 0, we must use division lemma to 13 and 52, to get

52 = 13 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 13.Therefore, the HCF of 52 and 65 is equal to 13

Notice that 13 = HCF(52,13) = HCF(65,52) .

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 91 and 13 because 91 is greater than 13

91 = 13 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 13.Therefore, the HCF of 13 and 91 is equal to 13

Notice that 13 = HCF(91,13) .

Result

Hence, the HCF of 52, 65, 91 is equal to 13.

FAQ on HCF of 52, 65, 91 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 52, 65, 91?

Answer: The HCF of 52, 65, 91 is 13.