HCF of 12345, 67890 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 12345, 67890 ? 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 12345, 67890 using Euclid's algorithm i.e 15 quickly.
Detailed Method to Find the HCF of 12345,67890 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 12345,67890. This is how to do it.
Step 1: The first step is to use the division lemma with 67890 and 12345 because 67890 is greater than 12345
67890 = 12345 x 5 + 6165
Step 2: Here, the reminder 12345 is not 0, we must use division lemma to 6165 and 12345, to get
12345 = 6165 x 2 + 15
Step 3: We consider the new divisor 6165 and the new remainder 15, and apply the division lemma to get
6165 = 15 x 411 + 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 15.Therefore, the HCF of 12345 and 67890 is equal to 15
Notice that 15 = HCF(6165,15) = HCF(12345,6165) = HCF(67890,12345) .
Result
Hence, the HCF of 12345, 67890 is equal to 15.
FAQ on HCF of 12345, 67890 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 12345, 67890?
Answer: The HCF of 12345, 67890 is 15.