Highest Common Factor of 9114, 6821 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 9114, 6821 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9114, 6821 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 9114, 6821 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 9114, 6821 is 1.
HCF(9114, 6821) = 1
HCF of 9114, 6821 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9114, 6821 is 1.
Highest Common Factor of 9114,6821 is 1
Step 1: Since 9114 > 6821, we apply the division lemma to 9114 and 6821, to get
9114 = 6821 x 1 + 2293
Step 2: Since the reminder 6821 ≠ 0, we apply division lemma to 2293 and 6821, to get
6821 = 2293 x 2 + 2235
Step 3: We consider the new divisor 2293 and the new remainder 2235, and apply the division lemma to get
2293 = 2235 x 1 + 58
We consider the new divisor 2235 and the new remainder 58,and apply the division lemma to get
2235 = 58 x 38 + 31
We consider the new divisor 58 and the new remainder 31,and apply the division lemma to get
58 = 31 x 1 + 27
We consider the new divisor 31 and the new remainder 27,and apply the division lemma to get
31 = 27 x 1 + 4
We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get
27 = 4 x 6 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 9114 and 6821 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(58,31) = HCF(2235,58) = HCF(2293,2235) = HCF(6821,2293) = HCF(9114,6821) .
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Frequently Asked Questions on HCF of 9114, 6821 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 9114, 6821?
Answer: HCF of 9114, 6821 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9114, 6821 using Euclid's Algorithm?
Answer: For arbitrary numbers 9114, 6821 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.