# HCF of 16, 56, 12 using Euclid's algorithm

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 16, 56, 12 ? 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 16, 56, 12 using Euclid's algorithm i.e 4 quickly.

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### Detailed Method to Find the HCF of 16,56,12 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 16,56,12. This is how to do it.

Step 1: The first step is to use the division lemma with 56 and 16 because 56 is greater than 16

56 = 16 x 3 + 8

Step 2: Here, the reminder 16 is not 0, we must use division lemma to 8 and 16, to get

16 = 8 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 8.Therefore, the HCF of 16 and 56 is equal to 8

Notice that 8 = HCF(16,8) = HCF(56,16) .

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 12 and 8 because 12 is greater than 8

12 = 8 x 1 + 4

Step 2: Here, the reminder 8 is not 0, we must use division lemma to 4 and 8, to get

8 = 4 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 4.Therefore, the HCF of 8 and 12 is equal to 4

Notice that 4 = HCF(8,4) = HCF(12,8) .

### Result

Hence, the HCF of 16, 56, 12 is equal to 4.

### FAQ on HCF of 16, 56, 12 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 16, 56, 12?

Answer: The HCF of 16, 56, 12 is 4.