HCF of 55, 150 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 55, 150 ? 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 55, 150 using Euclid's algorithm i.e 5 quickly.
Detailed Method to Find the HCF of 55,150 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 55,150. This is how to do it.
Step 1: The first step is to use the division lemma with 150 and 55 because 150 is greater than 55
150 = 55 x 2 + 40
Step 2: Since the reminder 55 is not 0, we must use division lemma to 40 and 55, to get
55 = 40 x 1 + 15
Step 3: We consider the new divisor 40 and the new remainder 15, and apply the division lemma to get
40 = 15 x 2 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 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 5.Therefore, the HCF of 55 and 150 is equal to 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(55,40) = HCF(150,55) .
Result
Hence, the HCF of 55, 150 is equal to 5.
FAQ on HCF of 55, 150 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 55, 150?
Answer: The HCF of 55, 150 is 5.