Want to know how to use Euclid’s algorithm to find the HCF of 27, 45, 108, 126 ? 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 27, 45, 108, 126 using Euclid's algorithm i.e 9 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 27,45,108,126. This is how to do it.
Step 1: The first step is to use the division lemma with 45 and 27 because 45 is greater than 27
45 = 27 x 1 + 18
Step 2: Here, the reminder 27 is not 0, we must use division lemma to 18 and 27, to get
27 = 18 x 1 + 9
Step 3: 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 27 and 45 is equal to 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) .
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 108 and 9 because 108 is greater than 9
108 = 9 x 12 + 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 108 is equal to 9
Notice that 9 = HCF(108,9) .
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 126 and 9 because 126 is greater than 9
126 = 9 x 14 + 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 126 is equal to 9
Notice that 9 = HCF(126,9) .
Hence, the HCF of 27, 45, 108, 126 is equal to 9.
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 27, 45, 108, 126?
Answer: The HCF of 27, 45, 108, 126 is 9.