Highest Common Factor of 6997, 2254 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 6997, 2254 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6997, 2254 is 1 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 6997, 2254 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 6997, 2254 is 1.
HCF(6997, 2254) = 1
HCF of 6997, 2254 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6997, 2254 is 1.
Highest Common Factor of 6997,2254 is 1
Step 1: Since 6997 > 2254, we apply the division lemma to 6997 and 2254, to get
6997 = 2254 x 3 + 235
Step 2: Since the reminder 2254 ≠ 0, we apply division lemma to 235 and 2254, to get
2254 = 235 x 9 + 139
Step 3: We consider the new divisor 235 and the new remainder 139, and apply the division lemma to get
235 = 139 x 1 + 96
We consider the new divisor 139 and the new remainder 96,and apply the division lemma to get
139 = 96 x 1 + 43
We consider the new divisor 96 and the new remainder 43,and apply the division lemma to get
96 = 43 x 2 + 10
We consider the new divisor 43 and the new remainder 10,and apply the division lemma to get
43 = 10 x 4 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6997 and 2254 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(43,10) = HCF(96,43) = HCF(139,96) = HCF(235,139) = HCF(2254,235) = HCF(6997,2254) .
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Frequently Asked Questions on HCF of 6997, 2254 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 6997, 2254?
Answer: HCF of 6997, 2254 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6997, 2254 using Euclid's Algorithm?
Answer: For arbitrary numbers 6997, 2254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.