Want to know how to use Euclid’s algorithm to find the HCF of 135, 180, 225 ? 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 135, 180, 225 using Euclid's algorithm i.e 45 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 135,180,225. This is how to do it.
Step 1: The first step is to use the division lemma with 180 and 135 because 180 is greater than 135
180 = 135 x 1 + 45
Step 2: Here, the reminder 135 is not 0, we must use division lemma to 45 and 135, to get
135 = 45 x 3 + 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 45.Therefore, the HCF of 135 and 180 is equal to 45
Notice that 45 = HCF(135,45) = HCF(180,135) .
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 225 and 45 because 225 is greater than 45
225 = 45 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 45.Therefore, the HCF of 45 and 225 is equal to 45
Notice that 45 = HCF(225,45) .
Hence, the HCF of 135, 180, 225 is equal to 45.
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 135, 180, 225?
Answer: The HCF of 135, 180, 225 is 45.