Highest Common Factor of 8130, 6874 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 8130, 6874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8130, 6874 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 8130, 6874 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 8130, 6874 is 2.
HCF(8130, 6874) = 2
HCF of 8130, 6874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8130, 6874 is 2.
Highest Common Factor of 8130,6874 is 2
Step 1: Since 8130 > 6874, we apply the division lemma to 8130 and 6874, to get
8130 = 6874 x 1 + 1256
Step 2: Since the reminder 6874 ≠ 0, we apply division lemma to 1256 and 6874, to get
6874 = 1256 x 5 + 594
Step 3: We consider the new divisor 1256 and the new remainder 594, and apply the division lemma to get
1256 = 594 x 2 + 68
We consider the new divisor 594 and the new remainder 68,and apply the division lemma to get
594 = 68 x 8 + 50
We consider the new divisor 68 and the new remainder 50,and apply the division lemma to get
68 = 50 x 1 + 18
We consider the new divisor 50 and the new remainder 18,and apply the division lemma to get
50 = 18 x 2 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 8130 and 6874 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(50,18) = HCF(68,50) = HCF(594,68) = HCF(1256,594) = HCF(6874,1256) = HCF(8130,6874) .
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Frequently Asked Questions on HCF of 8130, 6874 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 8130, 6874?
Answer: HCF of 8130, 6874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8130, 6874 using Euclid's Algorithm?
Answer: For arbitrary numbers 8130, 6874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.