HCF of 702, 153, 405, 450 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 702, 153, 405, 450 ? 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 702, 153, 405, 450 using Euclid's algorithm i.e 9 quickly.
Detailed Method to Find the HCF of 702,153,405,450 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 702,153,405,450. This is how to do it.
Step 1: The first step is to use the division lemma with 702 and 153 because 702 is greater than 153
702 = 153 x 4 + 90
Step 2: Since the reminder 153 is not 0, we must use division lemma to 90 and 153, to get
153 = 90 x 1 + 63
Step 3: We consider the new divisor 90 and the new remainder 63, and apply the division lemma to get
90 = 63 x 1 + 27
We consider the new divisor 63 and the new remainder 27,and apply the division lemma to get
63 = 27 x 2 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 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 9.Therefore, the HCF of 702 and 153 is equal to 9
Notice that 9 = HCF(27,9) = HCF(63,27) = HCF(90,63) = HCF(153,90) = HCF(702,153) .
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 405 and 9 because 405 is greater than 9
405 = 9 x 45 + 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 9 and 405 is equal to 9
Notice that 9 = HCF(405,9) .
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 450 and 9 because 450 is greater than 9
450 = 9 x 50 + 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 9 and 450 is equal to 9
Notice that 9 = HCF(450,9) .
Result
Hence, the HCF of 702, 153, 405, 450 is equal to 9.
FAQ on HCF of 702, 153, 405, 450 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 702, 153, 405, 450?
Answer: The HCF of 702, 153, 405, 450 is 9.