How to find HCF of 105, 147, 189 using Euclid's Algorithm?

For arbitrary numbers 105, 147, 189 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 105, 147, 189 using Euclid's Algorithm?

For arbitrary numbers 105, 147, 189 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 105, 147, 189 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 105, 147, 189?

HCF of 105, 147, 189 is 21 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 105, 147, 189 ? 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 105, 147, 189 using Euclid's algorithm i.e 21 quickly.

Detailed Method to Find the HCF of 105,147,189 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 105,147,189. This is how to do it.

Step 1: The first step is to use the division lemma with 147 and 105 because 147 is greater than 105

147 = 105 x 1 + 42

Step 2: Here, the reminder 105 is not 0, we must use division lemma to 42 and 105, to get

105 = 42 x 2 + 21

Step 3: We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get

42 = 21 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 21.Therefore, the HCF of 105 and 147 is equal to 21

Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(147,105) .

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 189 and 21 because 189 is greater than 21

189 = 21 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 21.Therefore, the HCF of 21 and 189 is equal to 21

Notice that 21 = HCF(189,21) .

Result

Hence, the HCF of 105, 147, 189 is equal to 21.

FAQ on HCF of 105, 147, 189 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 105, 147, 189?

Answer: The HCF of 105, 147, 189 is 21.