Highest Common Factor of 8717, 3643 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 8717, 3643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8717, 3643 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 8717, 3643 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 8717, 3643 is 1.

HCF(8717, 3643) = 1

HCF of 8717, 3643 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 8717, 3643 is 1.

Highest Common Factor of 8717,3643 using Euclid's algorithm

Highest Common Factor of 8717,3643 is 1

Step 1: Since 8717 > 3643, we apply the division lemma to 8717 and 3643, to get

8717 = 3643 x 2 + 1431

Step 2: Since the reminder 3643 ≠ 0, we apply division lemma to 1431 and 3643, to get

3643 = 1431 x 2 + 781

Step 3: We consider the new divisor 1431 and the new remainder 781, and apply the division lemma to get

1431 = 781 x 1 + 650

We consider the new divisor 781 and the new remainder 650,and apply the division lemma to get

781 = 650 x 1 + 131

We consider the new divisor 650 and the new remainder 131,and apply the division lemma to get

650 = 131 x 4 + 126

We consider the new divisor 131 and the new remainder 126,and apply the division lemma to get

131 = 126 x 1 + 5

We consider the new divisor 126 and the new remainder 5,and apply the division lemma to get

126 = 5 x 25 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8717 and 3643 is 1

Notice that 1 = HCF(5,1) = HCF(126,5) = HCF(131,126) = HCF(650,131) = HCF(781,650) = HCF(1431,781) = HCF(3643,1431) = HCF(8717,3643) .

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Frequently Asked Questions on HCF of 8717, 3643 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 8717, 3643?

Answer: HCF of 8717, 3643 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8717, 3643 using Euclid's Algorithm?

Answer: For arbitrary numbers 8717, 3643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.