How to find HCF of 108, 180, 288 using Euclid's Algorithm?

For arbitrary numbers 108, 180, 288 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 108, 180, 288 using Euclid's Algorithm?

For arbitrary numbers 108, 180, 288 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 108, 180, 288 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 108, 180, 288?

HCF of 108, 180, 288 is 36 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 108, 180, 288 ? 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 108, 180, 288 using Euclid's algorithm i.e 36 quickly.

Detailed Method to Find the HCF of 108,180,288 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 108,180,288. This is how to do it.

Step 1: The first step is to use the division lemma with 180 and 108 because 180 is greater than 108

180 = 108 x 1 + 72

Step 2: Here, the reminder 108 is not 0, we must use division lemma to 72 and 108, to get

108 = 72 x 1 + 36

Step 3: We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get

72 = 36 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 36.Therefore, the HCF of 108 and 180 is equal to 36

Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(180,108) .

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 288 and 36 because 288 is greater than 36

288 = 36 x 8 + 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 36.Therefore, the HCF of 36 and 288 is equal to 36

Notice that 36 = HCF(288,36) .

Result

Hence, the HCF of 108, 180, 288 is equal to 36.

FAQ on HCF of 108, 180, 288 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 108, 180, 288?

Answer: The HCF of 108, 180, 288 is 36.