How to find HCF of 28, 42, 56 using Euclid's Algorithm?

For arbitrary numbers 28, 42, 56 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 28, 42, 56 using Euclid's Algorithm?

For arbitrary numbers 28, 42, 56 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 28, 42, 56 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 28, 42, 56?

HCF of 28, 42, 56 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 28, 42, 56 ? 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 28, 42, 56 using Euclid's algorithm i.e 14 quickly.

Detailed Method to Find the HCF of 28,42,56 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 28,42,56. This is how to do it.

Step 1: The first step is to use the division lemma with 42 and 28 because 42 is greater than 28

42 = 28 x 1 + 14

Step 2: Here, the reminder 28 is not 0, we must use division lemma to 14 and 28, 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 28 and 42 is equal to 14

Notice that 14 = HCF(28,14) = HCF(42,28) .

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 56 and 14 because 56 is greater than 14

56 = 14 x 4 + 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 56 is equal to 14

Notice that 14 = HCF(56,14) .

Result

Hence, the HCF of 28, 42, 56 is equal to 14.

FAQ on HCF of 28, 42, 56 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 28, 42, 56?

Answer: The HCF of 28, 42, 56 is 14.