Want to know how to use Euclid’s algorithm to find the HCF of 105, 128, 180 ? 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 105, 128, 180 using Euclid's algorithm i.e 1 quickly.
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 105,128,180. This is how to do it.
Step 1: The first step is to use the division lemma with 128 and 105 because 128 is greater than 105
128 = 105 x 1 + 23
Step 2: Since the reminder 105 is not 0, we must use division lemma to 23 and 105, to get
105 = 23 x 4 + 13
Step 3: We consider the new divisor 23 and the new remainder 13, and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 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 1.Therefore, the HCF of 105 and 128 is equal to 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(105,23) = HCF(128,105) .
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 180 and 1 because 180 is greater than 1
180 = 1 x 180 + 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 1.Therefore, the HCF of 1 and 180 is equal to 1
Notice that 1 = HCF(180,1) .
Hence, the HCF of 105, 128, 180 is equal to 1.
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 105, 128, 180?
Answer: The HCF of 105, 128, 180 is 1.