Highest Common Factor of 6643, 8654, 57673 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 6643, 8654, 57673 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6643, 8654, 57673 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 6643, 8654, 57673 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 6643, 8654, 57673 is 1.
HCF(6643, 8654, 57673) = 1
HCF of 6643, 8654, 57673 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6643, 8654, 57673 is 1.
Highest Common Factor of 6643,8654,57673 is 1
Step 1: Since 8654 > 6643, we apply the division lemma to 8654 and 6643, to get
8654 = 6643 x 1 + 2011
Step 2: Since the reminder 6643 ≠ 0, we apply division lemma to 2011 and 6643, to get
6643 = 2011 x 3 + 610
Step 3: We consider the new divisor 2011 and the new remainder 610, and apply the division lemma to get
2011 = 610 x 3 + 181
We consider the new divisor 610 and the new remainder 181,and apply the division lemma to get
610 = 181 x 3 + 67
We consider the new divisor 181 and the new remainder 67,and apply the division lemma to get
181 = 67 x 2 + 47
We consider the new divisor 67 and the new remainder 47,and apply the division lemma to get
67 = 47 x 1 + 20
We consider the new divisor 47 and the new remainder 20,and apply the division lemma to get
47 = 20 x 2 + 7
We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6643 and 8654 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(47,20) = HCF(67,47) = HCF(181,67) = HCF(610,181) = HCF(2011,610) = HCF(6643,2011) = HCF(8654,6643) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57673 > 1, we apply the division lemma to 57673 and 1, to get
57673 = 1 x 57673 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57673 is 1
Notice that 1 = HCF(57673,1) .
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Frequently Asked Questions on HCF of 6643, 8654, 57673 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 6643, 8654, 57673?
Answer: HCF of 6643, 8654, 57673 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6643, 8654, 57673 using Euclid's Algorithm?
Answer: For arbitrary numbers 6643, 8654, 57673 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.