HCF of 303, 804, 579, 421 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 303, 804, 579, 421 ? 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 303, 804, 579, 421 using Euclid's algorithm i.e 1 quickly.
Detailed Method to Find the HCF of 303,804,579,421 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 303,804,579,421. This is how to do it.
Step 1: The first step is to use the division lemma with 804 and 303 because 804 is greater than 303
804 = 303 x 2 + 198
Step 2: Since the reminder 303 is not 0, we must use division lemma to 198 and 303, to get
303 = 198 x 1 + 105
Step 3: We consider the new divisor 198 and the new remainder 105, and apply the division lemma to get
198 = 105 x 1 + 93
We consider the new divisor 105 and the new remainder 93,and apply the division lemma to get
105 = 93 x 1 + 12
We consider the new divisor 93 and the new remainder 12,and apply the division lemma to get
93 = 12 x 7 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 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 3.Therefore, the HCF of 303 and 804 is equal to 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(93,12) = HCF(105,93) = HCF(198,105) = HCF(303,198) = HCF(804,303) .
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 579 and 3 because 579 is greater than 3
579 = 3 x 193 + 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 3.Therefore, the HCF of 3 and 579 is equal to 3
Notice that 3 = HCF(579,3) .
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 421 and 3 because 421 is greater than 3
421 = 3 x 140 + 1
Step 2: Here, the reminder 3 is not 0, we must use division lemma to 1 and 3, to get
3 = 1 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 1.Therefore, the HCF of 3 and 421 is equal to 1
Notice that 1 = HCF(3,1) = HCF(421,3) .
Result
Hence, the HCF of 303, 804, 579, 421 is equal to 1.
FAQ on HCF of 303, 804, 579, 421 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 303, 804, 579, 421?
Answer: The HCF of 303, 804, 579, 421 is 1.