Highest Common Factor of 6665, 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 6665, 6821 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6665, 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 6665, 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 6665, 6821 is 1.
HCF(6665, 6821) = 1
HCF of 6665, 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 6665, 6821 is 1.
Highest Common Factor of 6665,6821 is 1
Step 1: Since 6821 > 6665, we apply the division lemma to 6821 and 6665, to get
6821 = 6665 x 1 + 156
Step 2: Since the reminder 6665 ≠ 0, we apply division lemma to 156 and 6665, to get
6665 = 156 x 42 + 113
Step 3: We consider the new divisor 156 and the new remainder 113, and apply the division lemma to get
156 = 113 x 1 + 43
We consider the new divisor 113 and the new remainder 43,and apply the division lemma to get
113 = 43 x 2 + 27
We consider the new divisor 43 and the new remainder 27,and apply the division lemma to get
43 = 27 x 1 + 16
We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get
27 = 16 x 1 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6665 and 6821 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(43,27) = HCF(113,43) = HCF(156,113) = HCF(6665,156) = HCF(6821,6665) .
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Frequently Asked Questions on HCF of 6665, 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 6665, 6821?
Answer: HCF of 6665, 6821 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6665, 6821 using Euclid's Algorithm?
Answer: For arbitrary numbers 6665, 6821 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.