HCF of 200008, 500096 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 200008, 500096 ? 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 200008, 500096 using Euclid's algorithm i.e 8 quickly.
Detailed Method to Find the HCF of 200008,500096 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 200008,500096. This is how to do it.
Step 1: The first step is to use the division lemma with 500096 and 200008 because 500096 is greater than 200008
500096 = 200008 x 2 + 100080
Step 2: Since the reminder 200008 is not 0, we must use division lemma to 100080 and 200008, to get
200008 = 100080 x 1 + 99928
Step 3: We consider the new divisor 100080 and the new remainder 99928, and apply the division lemma to get
100080 = 99928 x 1 + 152
We consider the new divisor 99928 and the new remainder 152,and apply the division lemma to get
99928 = 152 x 657 + 64
We consider the new divisor 152 and the new remainder 64,and apply the division lemma to get
152 = 64 x 2 + 24
We consider the new divisor 64 and the new remainder 24,and apply the division lemma to get
64 = 24 x 2 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 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 8.Therefore, the HCF of 200008 and 500096 is equal to 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(152,64) = HCF(99928,152) = HCF(100080,99928) = HCF(200008,100080) = HCF(500096,200008) .
Result
Hence, the HCF of 200008, 500096 is equal to 8.
FAQ on HCF of 200008, 500096 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 200008, 500096?
Answer: The HCF of 200008, 500096 is 8.