How to find HCF of 98, 168, 182 using Euclid's Algorithm?

For arbitrary numbers 98, 168, 182 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 98, 168, 182 using Euclid's Algorithm?

For arbitrary numbers 98, 168, 182 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 98, 168, 182 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 98, 168, 182?

HCF of 98, 168, 182 is 14 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 98, 168, 182 ? 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 98, 168, 182 using Euclid's algorithm i.e 14 quickly.

Detailed Method to Find the HCF of 98,168,182 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 98,168,182. This is how to do it.

Step 1: The first step is to use the division lemma with 168 and 98 because 168 is greater than 98

168 = 98 x 1 + 70

Step 2: Here, the reminder 98 is not 0, we must use division lemma to 70 and 98, to get

98 = 70 x 1 + 28

Step 3: We consider the new divisor 70 and the new remainder 28, and apply the division lemma to get

70 = 28 x 2 + 14

We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get

28 = 14 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 14.Therefore, the HCF of 98 and 168 is equal to 14

Notice that 14 = HCF(28,14) = HCF(70,28) = HCF(98,70) = HCF(168,98) .

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 182 and 14 because 182 is greater than 14

182 = 14 x 13 + 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 14.Therefore, the HCF of 14 and 182 is equal to 14

Notice that 14 = HCF(182,14) .

Result

Hence, the HCF of 98, 168, 182 is equal to 14.

FAQ on HCF of 98, 168, 182 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 98, 168, 182?

Answer: The HCF of 98, 168, 182 is 14.