HCF of 675, 459, 99 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 675, 459, 99 ? 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 675, 459, 99 using Euclid's algorithm i.e 9 quickly.
Detailed Method to Find the HCF of 675,459,99 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 675,459,99. This is how to do it.
Step 1: The first step is to use the division lemma with 675 and 459 because 675 is greater than 459
675 = 459 x 1 + 216
Step 2: Here, the reminder 459 is not 0, we must use division lemma to 216 and 459, to get
459 = 216 x 2 + 27
Step 3: We consider the new divisor 216 and the new remainder 27, and apply the division lemma to get
216 = 27 x 8 + 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 27.Therefore, the HCF of 675 and 459 is equal to 27
Notice that 27 = HCF(216,27) = HCF(459,216) = HCF(675,459) .
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 99 and 27 because 99 is greater than 27
99 = 27 x 3 + 18
Step 2: Here, the reminder 27 is not 0, we must use division lemma to 18 and 27, to get
27 = 18 x 1 + 9
Step 3: We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 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 9.Therefore, the HCF of 27 and 99 is equal to 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(99,27) .
Result
Hence, the HCF of 675, 459, 99 is equal to 9.
FAQ on HCF of 675, 459, 99 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 675, 459, 99?
Answer: The HCF of 675, 459, 99 is 9.