How to find HCF of 64, 18, 30, 6 using Euclid's Algorithm?

For arbitrary numbers 64, 18, 30, 6 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 64, 18, 30, 6 using Euclid's Algorithm?

For arbitrary numbers 64, 18, 30, 6 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 64, 18, 30, 6 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 64, 18, 30, 6?

HCF of 64, 18, 30, 6 is 2 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 64, 18, 30, 6 ? 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 64, 18, 30, 6 using Euclid's algorithm i.e 2 quickly.

Detailed Method to Find the HCF of 64,18,30,6 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 64,18,30,6. This is how to do it.

Step 1: The first step is to use the division lemma with 64 and 18 because 64 is greater than 18

64 = 18 x 3 + 10

Step 2: Here, the reminder 18 is not 0, we must use division lemma to 10 and 18, to get

18 = 10 x 1 + 8

Step 3: We consider the new divisor 10 and the new remainder 8, and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get

8 = 2 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 2.Therefore, the HCF of 64 and 18 is equal to 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(64,18) .

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 30 and 2 because 30 is greater than 2

30 = 2 x 15 + 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 2.Therefore, the HCF of 2 and 30 is equal to 2

Notice that 2 = HCF(30,2) .

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 6 and 2 because 6 is greater than 2

6 = 2 x 3 + 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 2.Therefore, the HCF of 2 and 6 is equal to 2

Notice that 2 = HCF(6,2) .

Result

Hence, the HCF of 64, 18, 30, 6 is equal to 2.

FAQ on HCF of 64, 18, 30, 6 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 64, 18, 30, 6?

Answer: The HCF of 64, 18, 30, 6 is 2.