Highest Common Factor of 2998, 6806 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 2998, 6806 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2998, 6806 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 2998, 6806 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 2998, 6806 is 2.
HCF(2998, 6806) = 2
HCF of 2998, 6806 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2998, 6806 is 2.
Highest Common Factor of 2998,6806 is 2
Step 1: Since 6806 > 2998, we apply the division lemma to 6806 and 2998, to get
6806 = 2998 x 2 + 810
Step 2: Since the reminder 2998 ≠ 0, we apply division lemma to 810 and 2998, to get
2998 = 810 x 3 + 568
Step 3: We consider the new divisor 810 and the new remainder 568, and apply the division lemma to get
810 = 568 x 1 + 242
We consider the new divisor 568 and the new remainder 242,and apply the division lemma to get
568 = 242 x 2 + 84
We consider the new divisor 242 and the new remainder 84,and apply the division lemma to get
242 = 84 x 2 + 74
We consider the new divisor 84 and the new remainder 74,and apply the division lemma to get
84 = 74 x 1 + 10
We consider the new divisor 74 and the new remainder 10,and apply the division lemma to get
74 = 10 x 7 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 2998 and 6806 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(74,10) = HCF(84,74) = HCF(242,84) = HCF(568,242) = HCF(810,568) = HCF(2998,810) = HCF(6806,2998) .
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Frequently Asked Questions on HCF of 2998, 6806 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 2998, 6806?
Answer: HCF of 2998, 6806 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2998, 6806 using Euclid's Algorithm?
Answer: For arbitrary numbers 2998, 6806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.