HCF of 900, 572, 369, 814 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 900, 572, 369, 814 ? 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 900, 572, 369, 814 using Euclid's algorithm i.e 1 quickly.
Detailed Method to Find the HCF of 900,572,369,814 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 900,572,369,814. This is how to do it.
Step 1: The first step is to use the division lemma with 900 and 572 because 900 is greater than 572
900 = 572 x 1 + 328
Step 2: Since the reminder 572 is not 0, we must use division lemma to 328 and 572, to get
572 = 328 x 1 + 244
Step 3: We consider the new divisor 328 and the new remainder 244, and apply the division lemma to get
328 = 244 x 1 + 84
We consider the new divisor 244 and the new remainder 84,and apply the division lemma to get
244 = 84 x 2 + 76
We consider the new divisor 84 and the new remainder 76,and apply the division lemma to get
84 = 76 x 1 + 8
We consider the new divisor 76 and the new remainder 8,and apply the division lemma to get
76 = 8 x 9 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma 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 900 and 572 is equal to 4
Notice that 4 = HCF(8,4) = HCF(76,8) = HCF(84,76) = HCF(244,84) = HCF(328,244) = HCF(572,328) = HCF(900,572) .
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 369 and 4 because 369 is greater than 4
369 = 4 x 92 + 1
Step 2: Here, the reminder 4 is not 0, we must use division lemma to 1 and 4, to get
4 = 1 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 1.Therefore, the HCF of 4 and 369 is equal to 1
Notice that 1 = HCF(4,1) = HCF(369,4) .
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 814 and 1 because 814 is greater than 1
814 = 1 x 814 + 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 1.Therefore, the HCF of 1 and 814 is equal to 1
Notice that 1 = HCF(814,1) .
Result
Hence, the HCF of 900, 572, 369, 814 is equal to 1.
FAQ on HCF of 900, 572, 369, 814 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 900, 572, 369, 814?
Answer: The HCF of 900, 572, 369, 814 is 1.