How to find HCF of 3672, 2712 using Euclid's Algorithm?

For arbitrary numbers 3672, 2712 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 3672, 2712 using Euclid's Algorithm?

For arbitrary numbers 3672, 2712 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 3672, 2712 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 3672, 2712?

HCF of 3672, 2712 is 24 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 3672, 2712 ? 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 3672, 2712 using Euclid's algorithm i.e 24 quickly.

Detailed Method to Find the HCF of 3672,2712 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 3672,2712. This is how to do it.

Step 1: The first step is to use the division lemma with 3672 and 2712 because 3672 is greater than 2712

3672 = 2712 x 1 + 960

Step 2: Since the reminder 2712 is not 0, we must use division lemma to 960 and 2712, to get

2712 = 960 x 2 + 792

Step 3: We consider the new divisor 960 and the new remainder 792, and apply the division lemma to get

960 = 792 x 1 + 168

We consider the new divisor 792 and the new remainder 168,and apply the division lemma to get

792 = 168 x 4 + 120

We consider the new divisor 168 and the new remainder 120,and apply the division lemma to get

168 = 120 x 1 + 48

We consider the new divisor 120 and the new remainder 48,and apply the division lemma to get

120 = 48 x 2 + 24

We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get

48 = 24 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 24.Therefore, the HCF of 3672 and 2712 is equal to 24

Notice that 24 = HCF(48,24) = HCF(120,48) = HCF(168,120) = HCF(792,168) = HCF(960,792) = HCF(2712,960) = HCF(3672,2712) .

Result

Hence, the HCF of 3672, 2712 is equal to 24.

FAQ on HCF of 3672, 2712 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 3672, 2712?

Answer: The HCF of 3672, 2712 is 24.