Want to know how to use Euclid’s algorithm to find the HCF of 992, 392, 306, 338 ? 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 992, 392, 306, 338 using Euclid's algorithm i.e 2 quickly.
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 992,392,306,338. This is how to do it.
Step 1: The first step is to use the division lemma with 992 and 392 because 992 is greater than 392
992 = 392 x 2 + 208
Step 2: Since the reminder 392 is not 0, we must use division lemma to 208 and 392, to get
392 = 208 x 1 + 184
Step 3: We consider the new divisor 208 and the new remainder 184, and apply the division lemma to get
208 = 184 x 1 + 24
We consider the new divisor 184 and the new remainder 24,and apply the division lemma to get
184 = 24 x 7 + 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 992 and 392 is equal to 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(184,24) = HCF(208,184) = HCF(392,208) = HCF(992,392) .
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 306 and 8 because 306 is greater than 8
306 = 8 x 38 + 2
Step 2: Here, the reminder 8 is not 0, we must use division lemma to 2 and 8, to get
8 = 2 x 4 + 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 2.Therefore, the HCF of 8 and 306 is equal to 2
Notice that 2 = HCF(8,2) = HCF(306,8) .
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 338 and 2 because 338 is greater than 2
338 = 2 x 169 + 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 2.Therefore, the HCF of 2 and 338 is equal to 2
Notice that 2 = HCF(338,2) .
Hence, the HCF of 992, 392, 306, 338 is equal to 2.
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 992, 392, 306, 338?
Answer: The HCF of 992, 392, 306, 338 is 2.