How to find HCF of 20, 50, 100 using Euclid's Algorithm?

For arbitrary numbers 20, 50, 100 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 20, 50, 100 using Euclid's Algorithm?

For arbitrary numbers 20, 50, 100 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 20, 50, 100 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 20, 50, 100?

HCF of 20, 50, 100 is 10 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 20, 50, 100 ? 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 20, 50, 100 using Euclid's algorithm i.e 10 quickly.

Detailed Method to Find the HCF of 20,50,100 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 20,50,100. This is how to do it.

Step 1: The first step is to use the division lemma with 50 and 20 because 50 is greater than 20

50 = 20 x 2 + 10

Step 2: Here, the reminder 20 is not 0, we must use division lemma to 10 and 20, to get

20 = 10 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 10.Therefore, the HCF of 20 and 50 is equal to 10

Notice that 10 = HCF(20,10) = HCF(50,20) .

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 100 and 10 because 100 is greater than 10

100 = 10 x 10 + 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 10.Therefore, the HCF of 10 and 100 is equal to 10

Notice that 10 = HCF(100,10) .

Result

Hence, the HCF of 20, 50, 100 is equal to 10.

FAQ on HCF of 20, 50, 100 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 20, 50, 100?

Answer: The HCF of 20, 50, 100 is 10.