How to find HCF of 34, 51, 85 using Euclid's Algorithm?

For arbitrary numbers 34, 51, 85 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 34, 51, 85 using Euclid's Algorithm?

For arbitrary numbers 34, 51, 85 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 34, 51, 85 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 34, 51, 85?

HCF of 34, 51, 85 is 17 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 34, 51, 85 ? 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 34, 51, 85 using Euclid's algorithm i.e 17 quickly.

Detailed Method to Find the HCF of 34,51,85 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 34,51,85. This is how to do it.

Step 1: The first step is to use the division lemma with 51 and 34 because 51 is greater than 34

51 = 34 x 1 + 17

Step 2: Here, the reminder 34 is not 0, we must use division lemma to 17 and 34, to get

34 = 17 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 17.Therefore, the HCF of 34 and 51 is equal to 17

Notice that 17 = HCF(34,17) = HCF(51,34) .

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 85 and 17 because 85 is greater than 17

85 = 17 x 5 + 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 17.Therefore, the HCF of 17 and 85 is equal to 17

Notice that 17 = HCF(85,17) .

Result

Hence, the HCF of 34, 51, 85 is equal to 17.

FAQ on HCF of 34, 51, 85 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 34, 51, 85?

Answer: The HCF of 34, 51, 85 is 17.