HCF of 70, 820, 670, 215 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 70, 820, 670, 215 ? 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 70, 820, 670, 215 using Euclid's algorithm i.e 5 quickly.
Detailed Method to Find the HCF of 70,820,670,215 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 70,820,670,215. This is how to do it.
Step 1: The first step is to use the division lemma with 820 and 70 because 820 is greater than 70
820 = 70 x 11 + 50
Step 2: Here, the reminder 70 is not 0, we must use division lemma to 50 and 70, to get
70 = 50 x 1 + 20
Step 3: We consider the new divisor 50 and the new remainder 20, and apply the division lemma to get
50 = 20 x 2 + 10
We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 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 10.Therefore, the HCF of 70 and 820 is equal to 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(70,50) = HCF(820,70) .
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 670 and 10 because 670 is greater than 10
670 = 10 x 67 + 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 10.Therefore, the HCF of 10 and 670 is equal to 10
Notice that 10 = HCF(670,10) .
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 215 and 10 because 215 is greater than 10
215 = 10 x 21 + 5
Step 2: Here, the reminder 10 is not 0, we must use division lemma to 5 and 10, to get
10 = 5 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 5.Therefore, the HCF of 10 and 215 is equal to 5
Notice that 5 = HCF(10,5) = HCF(215,10) .
Result
Hence, the HCF of 70, 820, 670, 215 is equal to 5.
FAQ on HCF of 70, 820, 670, 215 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 70, 820, 670, 215?
Answer: The HCF of 70, 820, 670, 215 is 5.