Want to know how to use Euclid’s algorithm to find the HCF of 72, 46, 65 ? 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 72, 46, 65 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 72,46,65. This is how to do it.
Step 1: The first step is to use the division lemma with 72 and 46 because 72 is greater than 46
72 = 46 x 1 + 26
Step 2: Since the reminder 46 is not 0, we must use division lemma to 26 and 46, to get
46 = 26 x 1 + 20
Step 3: We consider the new divisor 26 and the new remainder 20, and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 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 2.Therefore, the HCF of 72 and 46 is equal to 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(72,46) .
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 65 and 2 because 65 is greater than 2
65 = 2 x 32 + 1
Step 2: Here, the reminder 2 is not 0, we must use division lemma to 1 and 2, 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 2 and 65 is equal to 1
Notice that 1 = HCF(2,1) = HCF(65,2) .
Hence, the HCF of 72, 46, 65 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 72, 46, 65?
Answer: The HCF of 72, 46, 65 is 1.