HCF of 819, 486, 171, 189 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 819, 486, 171, 189 ? 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 819, 486, 171, 189 using Euclid's algorithm i.e 9 quickly.
Detailed Method to Find the HCF of 819,486,171,189 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 819,486,171,189. This is how to do it.
Step 1: The first step is to use the division lemma with 819 and 486 because 819 is greater than 486
819 = 486 x 1 + 333
Step 2: Since the reminder 486 is not 0, we must use division lemma to 333 and 486, to get
486 = 333 x 1 + 153
Step 3: We consider the new divisor 333 and the new remainder 153, and apply the division lemma to get
333 = 153 x 2 + 27
We consider the new divisor 153 and the new remainder 27,and apply the division lemma to get
153 = 27 x 5 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma 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 819 and 486 is equal to 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(153,27) = HCF(333,153) = HCF(486,333) = HCF(819,486) .
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 171 and 9 because 171 is greater than 9
171 = 9 x 19 + 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 171 is equal to 9
Notice that 9 = HCF(171,9) .
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 189 and 9 because 189 is greater than 9
189 = 9 x 21 + 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 189 is equal to 9
Notice that 9 = HCF(189,9) .
Result
Hence, the HCF of 819, 486, 171, 189 is equal to 9.
FAQ on HCF of 819, 486, 171, 189 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 819, 486, 171, 189?
Answer: The HCF of 819, 486, 171, 189 is 9.