HCF of 100, 105, 125, 128 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 100, 105, 125, 128 ? 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 100, 105, 125, 128 using Euclid's algorithm i.e 1 quickly.
Detailed Method to Find the HCF of 100,105,125,128 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 100,105,125,128. This is how to do it.
Step 1: The first step is to use the division lemma with 105 and 100 because 105 is greater than 100
105 = 100 x 1 + 5
Step 2: Here, the reminder 100 is not 0, we must use division lemma to 5 and 100, to get
100 = 5 x 20 + 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 5.Therefore, the HCF of 100 and 105 is equal to 5
Notice that 5 = HCF(100,5) = HCF(105,100) .
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 125 and 5 because 125 is greater than 5
125 = 5 x 25 + 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 5.Therefore, the HCF of 5 and 125 is equal to 5
Notice that 5 = HCF(125,5) .
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 128 and 5 because 128 is greater than 5
128 = 5 x 25 + 3
Step 2: Here, the reminder 5 is not 0, we must use division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 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 1.Therefore, the HCF of 5 and 128 is equal to 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(128,5) .
Result
Hence, the HCF of 100, 105, 125, 128 is equal to 1.
FAQ on HCF of 100, 105, 125, 128 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 100, 105, 125, 128?
Answer: The HCF of 100, 105, 125, 128 is 1.