Highest Common Factor of 8654, 6140 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 8654, 6140 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8654, 6140 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 8654, 6140 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 8654, 6140 is 2.
HCF(8654, 6140) = 2
HCF of 8654, 6140 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8654, 6140 is 2.
Highest Common Factor of 8654,6140 is 2
Step 1: Since 8654 > 6140, we apply the division lemma to 8654 and 6140, to get
8654 = 6140 x 1 + 2514
Step 2: Since the reminder 6140 ≠ 0, we apply division lemma to 2514 and 6140, to get
6140 = 2514 x 2 + 1112
Step 3: We consider the new divisor 2514 and the new remainder 1112, and apply the division lemma to get
2514 = 1112 x 2 + 290
We consider the new divisor 1112 and the new remainder 290,and apply the division lemma to get
1112 = 290 x 3 + 242
We consider the new divisor 290 and the new remainder 242,and apply the division lemma to get
290 = 242 x 1 + 48
We consider the new divisor 242 and the new remainder 48,and apply the division lemma to get
242 = 48 x 5 + 2
We consider the new divisor 48 and the new remainder 2,and apply the division lemma to get
48 = 2 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8654 and 6140 is 2
Notice that 2 = HCF(48,2) = HCF(242,48) = HCF(290,242) = HCF(1112,290) = HCF(2514,1112) = HCF(6140,2514) = HCF(8654,6140) .
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Frequently Asked Questions on HCF of 8654, 6140 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 8654, 6140?
Answer: HCF of 8654, 6140 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8654, 6140 using Euclid's Algorithm?
Answer: For arbitrary numbers 8654, 6140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.