HCF of 78, 156, 169 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 78, 156, 169 ? 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 78, 156, 169 using Euclid's algorithm i.e 13 quickly.
Detailed Method to Find the HCF of 78,156,169 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 78,156,169. This is how to do it.
Step 1: The first step is to use the division lemma with 156 and 78 because 156 is greater than 78
156 = 78 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 78.Therefore, the HCF of 78 and 156 is equal to 78
Notice that 78 = HCF(156,78) .
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 169 and 78 because 169 is greater than 78
169 = 78 x 2 + 13
Step 2: Here, the reminder 78 is not 0, we must use division lemma to 13 and 78, to get
78 = 13 x 6 + 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 13.Therefore, the HCF of 78 and 169 is equal to 13
Notice that 13 = HCF(78,13) = HCF(169,78) .
Result
Hence, the HCF of 78, 156, 169 is equal to 13.
FAQ on HCF of 78, 156, 169 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 78, 156, 169?
Answer: The HCF of 78, 156, 169 is 13.