Want to know how to use Euclid’s algorithm to find the HCF of 50, 220, 242 ? 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 50, 220, 242 using Euclid's algorithm i.e 2 quickly.
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 50,220,242. This is how to do it.
Step 1: The first step is to use the division lemma with 220 and 50 because 220 is greater than 50
220 = 50 x 4 + 20
Step 2: Here, the reminder 50 is not 0, we must use division lemma to 20 and 50, to get
50 = 20 x 2 + 10
Step 3: 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 50 and 220 is equal to 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(220,50) .
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 242 and 10 because 242 is greater than 10
242 = 10 x 24 + 2
Step 2: Here, the reminder 10 is not 0, we must use division lemma to 2 and 10, to get
10 = 2 x 5 + 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 2.Therefore, the HCF of 10 and 242 is equal to 2
Notice that 2 = HCF(10,2) = HCF(242,10) .
Hence, the HCF of 50, 220, 242 is equal to 2.
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 50, 220, 242?
Answer: The HCF of 50, 220, 242 is 2.