Highest Common Factor of 8209, 9709 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 8209, 9709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8209, 9709 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 8209, 9709 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 8209, 9709 is 1.

HCF(8209, 9709) = 1

HCF of 8209, 9709 using Euclid's algorithm

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

HCF of:

Highest common factor (HCF) of 8209, 9709 is 1.

Highest Common Factor of 8209,9709 using Euclid's algorithm

Highest Common Factor of 8209,9709 is 1

Step 1: Since 9709 > 8209, we apply the division lemma to 9709 and 8209, to get

9709 = 8209 x 1 + 1500

Step 2: Since the reminder 8209 ≠ 0, we apply division lemma to 1500 and 8209, to get

8209 = 1500 x 5 + 709

Step 3: We consider the new divisor 1500 and the new remainder 709, and apply the division lemma to get

1500 = 709 x 2 + 82

We consider the new divisor 709 and the new remainder 82,and apply the division lemma to get

709 = 82 x 8 + 53

We consider the new divisor 82 and the new remainder 53,and apply the division lemma to get

82 = 53 x 1 + 29

We consider the new divisor 53 and the new remainder 29,and apply the division lemma to get

53 = 29 x 1 + 24

We consider the new divisor 29 and the new remainder 24,and apply the division lemma to get

29 = 24 x 1 + 5

We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get

24 = 5 x 4 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8209 and 9709 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(53,29) = HCF(82,53) = HCF(709,82) = HCF(1500,709) = HCF(8209,1500) = HCF(9709,8209) .

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Frequently Asked Questions on HCF of 8209, 9709 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 8209, 9709?

Answer: HCF of 8209, 9709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8209, 9709 using Euclid's Algorithm?

Answer: For arbitrary numbers 8209, 9709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.