Highest Common Factor of 2086, 2643 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 2086, 2643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2086, 2643 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 2086, 2643 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 2086, 2643 is 1.
HCF(2086, 2643) = 1
HCF of 2086, 2643 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2086, 2643 is 1.
Highest Common Factor of 2086,2643 is 1
Step 1: Since 2643 > 2086, we apply the division lemma to 2643 and 2086, to get
2643 = 2086 x 1 + 557
Step 2: Since the reminder 2086 ≠ 0, we apply division lemma to 557 and 2086, to get
2086 = 557 x 3 + 415
Step 3: We consider the new divisor 557 and the new remainder 415, and apply the division lemma to get
557 = 415 x 1 + 142
We consider the new divisor 415 and the new remainder 142,and apply the division lemma to get
415 = 142 x 2 + 131
We consider the new divisor 142 and the new remainder 131,and apply the division lemma to get
142 = 131 x 1 + 11
We consider the new divisor 131 and the new remainder 11,and apply the division lemma to get
131 = 11 x 11 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2086 and 2643 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(131,11) = HCF(142,131) = HCF(415,142) = HCF(557,415) = HCF(2086,557) = HCF(2643,2086) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2086, 2643 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 2086, 2643?
Answer: HCF of 2086, 2643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2086, 2643 using Euclid's Algorithm?
Answer: For arbitrary numbers 2086, 2643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.