How to find HCF of 51, 85, 153 using Euclid's Algorithm?

For arbitrary numbers 51, 85, 153 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 51, 85, 153 using Euclid's Algorithm?

For arbitrary numbers 51, 85, 153 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 51, 85, 153 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 51, 85, 153?

HCF of 51, 85, 153 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 51, 85, 153 ? 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 51, 85, 153 using Euclid's algorithm i.e 17 quickly.

Detailed Method to Find the HCF of 51,85,153 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 51,85,153. This is how to do it.

Step 1: The first step is to use the division lemma with 85 and 51 because 85 is greater than 51

85 = 51 x 1 + 34

Step 2: Here, the reminder 51 is not 0, we must use division lemma to 34 and 51, to get

51 = 34 x 1 + 17

Step 3: We consider the new divisor 34 and the new remainder 17, and apply the division lemma 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 51 and 85 is equal to 17

Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(85,51) .

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 153 and 17 because 153 is greater than 17

153 = 17 x 9 + 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 153 is equal to 17

Notice that 17 = HCF(153,17) .

Result

Hence, the HCF of 51, 85, 153 is equal to 17.

FAQ on HCF of 51, 85, 153 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 51, 85, 153?

Answer: The HCF of 51, 85, 153 is 17.