Highest Common Factor of 2046, 6842 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 2046, 6842 i.e. 22 the largest integer that leaves a remainder zero for all numbers.
HCF of 2046, 6842 is 22 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 2046, 6842 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 2046, 6842 is 22.
HCF(2046, 6842) = 22
HCF of 2046, 6842 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2046, 6842 is 22.
Highest Common Factor of 2046,6842 is 22
Step 1: Since 6842 > 2046, we apply the division lemma to 6842 and 2046, to get
6842 = 2046 x 3 + 704
Step 2: Since the reminder 2046 ≠ 0, we apply division lemma to 704 and 2046, to get
2046 = 704 x 2 + 638
Step 3: We consider the new divisor 704 and the new remainder 638, and apply the division lemma to get
704 = 638 x 1 + 66
We consider the new divisor 638 and the new remainder 66,and apply the division lemma to get
638 = 66 x 9 + 44
We consider the new divisor 66 and the new remainder 44,and apply the division lemma to get
66 = 44 x 1 + 22
We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get
44 = 22 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 2046 and 6842 is 22
Notice that 22 = HCF(44,22) = HCF(66,44) = HCF(638,66) = HCF(704,638) = HCF(2046,704) = HCF(6842,2046) .
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Frequently Asked Questions on HCF of 2046, 6842 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 2046, 6842?
Answer: HCF of 2046, 6842 is 22 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2046, 6842 using Euclid's Algorithm?
Answer: For arbitrary numbers 2046, 6842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
