HCF of 90, 500 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 90, 500 ? 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 90, 500 using Euclid's algorithm i.e 10 quickly.
Detailed Method to Find the HCF of 90,500 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 90,500. This is how to do it.
Step 1: The first step is to use the division lemma with 500 and 90 because 500 is greater than 90
500 = 90 x 5 + 50
Step 2: Here, the reminder 90 is not 0, we must use division lemma to 50 and 90, to get
90 = 50 x 1 + 40
Step 3: We consider the new divisor 50 and the new remainder 40, and apply the division lemma to get
50 = 40 x 1 + 10
We consider the new divisor 40 and the new remainder 10, and apply the division lemma to get
40 = 10 x 4 + 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 90 and 500 is equal to 10
Notice that 10 = HCF(40,10) = HCF(50,40) = HCF(90,50) = HCF(500,90) .
Result
Hence, the HCF of 90, 500 is equal to 10.
FAQ on HCF of 90, 500 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 90, 500?
Answer: The HCF of 90, 500 is 10.