HCF of 864, 504, 639, 468 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 864, 504, 639, 468 ? 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 864, 504, 639, 468 using Euclid's algorithm i.e 9 quickly.
Detailed Method to Find the HCF of 864,504,639,468 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 864,504,639,468. This is how to do it.
Step 1: The first step is to use the division lemma with 864 and 504 because 864 is greater than 504
864 = 504 x 1 + 360
Step 2: Here, the reminder 504 is not 0, we must use division lemma to 360 and 504, to get
504 = 360 x 1 + 144
Step 3: We consider the new divisor 360 and the new remainder 144, and apply the division lemma to get
360 = 144 x 2 + 72
We consider the new divisor 144 and the new remainder 72, and apply the division lemma to get
144 = 72 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 72.Therefore, the HCF of 864 and 504 is equal to 72
Notice that 72 = HCF(144,72) = HCF(360,144) = HCF(504,360) = HCF(864,504) .
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 639 and 72 because 639 is greater than 72
639 = 72 x 8 + 63
Step 2: Here, the reminder 72 is not 0, we must use division lemma to 63 and 72, to get
72 = 63 x 1 + 9
Step 3: We consider the new divisor 63 and the new remainder 9, and apply the division lemma to get
63 = 9 x 7 + 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 72 and 639 is equal to 9
Notice that 9 = HCF(63,9) = HCF(72,63) = HCF(639,72) .
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 468 and 9 because 468 is greater than 9
468 = 9 x 52 + 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 468 is equal to 9
Notice that 9 = HCF(468,9) .
Result
Hence, the HCF of 864, 504, 639, 468 is equal to 9.
FAQ on HCF of 864, 504, 639, 468 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 864, 504, 639, 468?
Answer: The HCF of 864, 504, 639, 468 is 9.