HCF of 57, 62, 21, 99 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 57, 62, 21, 99 ? 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 57, 62, 21, 99 using Euclid's algorithm i.e 1 quickly.
Detailed Method to Find the HCF of 57,62,21,99 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 57,62,21,99. This is how to do it.
Step 1: The first step is to use the division lemma with 62 and 57 because 62 is greater than 57
62 = 57 x 1 + 5
Step 2: Here, the reminder 57 is not 0, we must use division lemma to 5 and 57, to get
57 = 5 x 11 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 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 1.Therefore, the HCF of 57 and 62 is equal to 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(57,5) = HCF(62,57) .
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 21 and 1 because 21 is greater than 1
21 = 1 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 1.Therefore, the HCF of 1 and 21 is equal to 1
Notice that 1 = HCF(21,1) .
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 99 and 1 because 99 is greater than 1
99 = 1 x 99 + 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 99 is equal to 1
Notice that 1 = HCF(99,1) .
Result
Hence, the HCF of 57, 62, 21, 99 is equal to 1.
FAQ on HCF of 57, 62, 21, 99 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 57, 62, 21, 99?
Answer: The HCF of 57, 62, 21, 99 is 1.