HCF of 350, 500, 130, 260 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 350, 500, 130, 260 ? 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 350, 500, 130, 260 using Euclid's algorithm i.e 10 quickly.
Detailed Method to Find the HCF of 350,500,130,260 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 350,500,130,260. This is how to do it.
Step 1: The first step is to use the division lemma with 500 and 350 because 500 is greater than 350
500 = 350 x 1 + 150
Step 2: Here, the reminder 350 is not 0, we must use division lemma to 150 and 350, to get
350 = 150 x 2 + 50
Step 3: We consider the new divisor 150 and the new remainder 50, and apply the division lemma to get
150 = 50 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 50.Therefore, the HCF of 350 and 500 is equal to 50
Notice that 50 = HCF(150,50) = HCF(350,150) = HCF(500,350) .
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 130 and 50 because 130 is greater than 50
130 = 50 x 2 + 30
Step 2: Here, the reminder 50 is not 0, we must use division lemma to 30 and 50, to get
50 = 30 x 1 + 20
Step 3: We consider the new divisor 30 and the new remainder 20, and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 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 10.Therefore, the HCF of 50 and 130 is equal to 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(50,30) = HCF(130,50) .
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 260 and 10 because 260 is greater than 10
260 = 10 x 26 + 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 10 and 260 is equal to 10
Notice that 10 = HCF(260,10) .
Result
Hence, the HCF of 350, 500, 130, 260 is equal to 10.
FAQ on HCF of 350, 500, 130, 260 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 350, 500, 130, 260?
Answer: The HCF of 350, 500, 130, 260 is 10.