Want to know how to use Euclid’s algorithm to find the HCF of 108, 120, 144 ? 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 108, 120, 144 using Euclid's algorithm i.e 12 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 108,120,144. This is how to do it.
Step 1: The first step is to use the division lemma with 120 and 108 because 120 is greater than 108
120 = 108 x 1 + 12
Step 2: Here, the reminder 108 is not 0, we must use division lemma to 12 and 108, to get
108 = 12 x 9 + 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 12.Therefore, the HCF of 108 and 120 is equal to 12
Notice that 12 = HCF(108,12) = HCF(120,108) .
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 144 and 12 because 144 is greater than 12
144 = 12 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 12.Therefore, the HCF of 12 and 144 is equal to 12
Notice that 12 = HCF(144,12) .
Hence, the HCF of 108, 120, 144 is equal to 12.
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 108, 120, 144?
Answer: The HCF of 108, 120, 144 is 12.