Highest Common Factor of 684, 784, 206 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 684, 784, 206 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 784, 206 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 684, 784, 206 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 684, 784, 206 is 2.
HCF(684, 784, 206) = 2
HCF of 684, 784, 206 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 784, 206 is 2.
Highest Common Factor of 684,784,206 is 2
Step 1: Since 784 > 684, we apply the division lemma to 784 and 684, to get
784 = 684 x 1 + 100
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 100 and 684, to get
684 = 100 x 6 + 84
Step 3: We consider the new divisor 100 and the new remainder 84, and apply the division lemma to get
100 = 84 x 1 + 16
We consider the new divisor 84 and the new remainder 16,and apply the division lemma to get
84 = 16 x 5 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 684 and 784 is 4
Notice that 4 = HCF(16,4) = HCF(84,16) = HCF(100,84) = HCF(684,100) = HCF(784,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 206 > 4, we apply the division lemma to 206 and 4, to get
206 = 4 x 51 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 206 is 2
Notice that 2 = HCF(4,2) = HCF(206,4) .
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Frequently Asked Questions on HCF of 684, 784, 206 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 684, 784, 206?
Answer: HCF of 684, 784, 206 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 784, 206 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 784, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
