Highest Common Factor of 8006, 5814 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 8006, 5814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8006, 5814 is 2 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 8006, 5814 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 8006, 5814 is 2.
HCF(8006, 5814) = 2
HCF of 8006, 5814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8006, 5814 is 2.
Highest Common Factor of 8006,5814 is 2
Step 1: Since 8006 > 5814, we apply the division lemma to 8006 and 5814, to get
8006 = 5814 x 1 + 2192
Step 2: Since the reminder 5814 ≠ 0, we apply division lemma to 2192 and 5814, to get
5814 = 2192 x 2 + 1430
Step 3: We consider the new divisor 2192 and the new remainder 1430, and apply the division lemma to get
2192 = 1430 x 1 + 762
We consider the new divisor 1430 and the new remainder 762,and apply the division lemma to get
1430 = 762 x 1 + 668
We consider the new divisor 762 and the new remainder 668,and apply the division lemma to get
762 = 668 x 1 + 94
We consider the new divisor 668 and the new remainder 94,and apply the division lemma to get
668 = 94 x 7 + 10
We consider the new divisor 94 and the new remainder 10,and apply the division lemma to get
94 = 10 x 9 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8006 and 5814 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(94,10) = HCF(668,94) = HCF(762,668) = HCF(1430,762) = HCF(2192,1430) = HCF(5814,2192) = HCF(8006,5814) .
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Frequently Asked Questions on HCF of 8006, 5814 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 8006, 5814?
Answer: HCF of 8006, 5814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8006, 5814 using Euclid's Algorithm?
Answer: For arbitrary numbers 8006, 5814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.