HCF of 30, 78, 69, 12 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 30, 78, 69, 12 ? 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 30, 78, 69, 12 using Euclid's algorithm i.e 3 quickly.
Detailed Method to Find the HCF of 30,78,69,12 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 30,78,69,12. This is how to do it.
Step 1: The first step is to use the division lemma with 78 and 30 because 78 is greater than 30
78 = 30 x 2 + 18
Step 2: Here, the reminder 30 is not 0, we must use division lemma to 18 and 30, to get
30 = 18 x 1 + 12
Step 3: We consider the new divisor 18 and the new remainder 12, and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 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 6.Therefore, the HCF of 30 and 78 is equal to 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(78,30) .
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 69 and 6 because 69 is greater than 6
69 = 6 x 11 + 3
Step 2: Here, the reminder 6 is not 0, we must use division lemma to 3 and 6, to get
6 = 3 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 3.Therefore, the HCF of 6 and 69 is equal to 3
Notice that 3 = HCF(6,3) = HCF(69,6) .
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 12 and 3 because 12 is greater than 3
12 = 3 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 3.Therefore, the HCF of 3 and 12 is equal to 3
Notice that 3 = HCF(12,3) .
Result
Hence, the HCF of 30, 78, 69, 12 is equal to 3.
FAQ on HCF of 30, 78, 69, 12 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 30, 78, 69, 12?
Answer: The HCF of 30, 78, 69, 12 is 3.