HCF of 666, 504, 63, 612 using Euclid's algorithm
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Want to know how to use Euclid’s algorithm to find the HCF of 666, 504, 63, 612 ? 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 666, 504, 63, 612 using Euclid's algorithm i.e 9 quickly.
Detailed Method to Find the HCF of 666,504,63,612 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 666,504,63,612. This is how to do it.
Step 1: The first step is to use the division lemma with 666 and 504 because 666 is greater than 504
666 = 504 x 1 + 162
Step 2: Here, the reminder 504 is not 0, we must use division lemma to 162 and 504, to get
504 = 162 x 3 + 18
Step 3: We consider the new divisor 162 and the new remainder 18, and apply the division lemma to get
162 = 18 x 9 + 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 18.Therefore, the HCF of 666 and 504 is equal to 18
Notice that 18 = HCF(162,18) = HCF(504,162) = HCF(666,504) .
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 63 and 18 because 63 is greater than 18
63 = 18 x 3 + 9
Step 2: Here, the reminder 18 is not 0, we must use division lemma to 9 and 18, to get
18 = 9 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 9.Therefore, the HCF of 18 and 63 is equal to 9
Notice that 9 = HCF(18,9) = HCF(63,18) .
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 612 and 9 because 612 is greater than 9
612 = 9 x 68 + 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 9.Therefore, the HCF of 9 and 612 is equal to 9
Notice that 9 = HCF(612,9) .
Result
Hence, the HCF of 666, 504, 63, 612 is equal to 9.
FAQ on HCF of 666, 504, 63, 612 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 666, 504, 63, 612?
Answer: The HCF of 666, 504, 63, 612 is 9.