How to find HCF of 92, 854, 154 using Euclid's Algorithm?

For arbitrary numbers 92, 854, 154 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 92, 854, 154 using Euclid's Algorithm?

For arbitrary numbers 92, 854, 154 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 92, 854, 154 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 92, 854, 154?

HCF of 92, 854, 154 is 2 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 92, 854, 154 ? 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 92, 854, 154 using Euclid's algorithm i.e 2 quickly.

Detailed Method to Find the HCF of 92,854,154 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 92,854,154. This is how to do it.

Step 1: The first step is to use the division lemma with 854 and 92 because 854 is greater than 92

854 = 92 x 9 + 26

Step 2: Since the reminder 92 is not 0, we must use division lemma to 26 and 92, to get

92 = 26 x 3 + 14

Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 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 2.Therefore, the HCF of 92 and 854 is equal to 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(92,26) = HCF(854,92) .

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 154 and 2 because 154 is greater than 2

154 = 2 x 77 + 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 2.Therefore, the HCF of 2 and 154 is equal to 2

Notice that 2 = HCF(154,2) .

Result

Hence, the HCF of 92, 854, 154 is equal to 2.

FAQ on HCF of 92, 854, 154 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 92, 854, 154?

Answer: The HCF of 92, 854, 154 is 2.