Highest Common Factor of 7309, 1709 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 7309, 1709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7309, 1709 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 7309, 1709 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 7309, 1709 is 1.

HCF(7309, 1709) = 1

HCF of 7309, 1709 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 7309, 1709 is 1.

Highest Common Factor of 7309,1709 using Euclid's algorithm

Highest Common Factor of 7309,1709 is 1

Step 1: Since 7309 > 1709, we apply the division lemma to 7309 and 1709, to get

7309 = 1709 x 4 + 473

Step 2: Since the reminder 1709 ≠ 0, we apply division lemma to 473 and 1709, to get

1709 = 473 x 3 + 290

Step 3: We consider the new divisor 473 and the new remainder 290, and apply the division lemma to get

473 = 290 x 1 + 183

We consider the new divisor 290 and the new remainder 183,and apply the division lemma to get

290 = 183 x 1 + 107

We consider the new divisor 183 and the new remainder 107,and apply the division lemma to get

183 = 107 x 1 + 76

We consider the new divisor 107 and the new remainder 76,and apply the division lemma to get

107 = 76 x 1 + 31

We consider the new divisor 76 and the new remainder 31,and apply the division lemma to get

76 = 31 x 2 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7309 and 1709 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(76,31) = HCF(107,76) = HCF(183,107) = HCF(290,183) = HCF(473,290) = HCF(1709,473) = HCF(7309,1709) .

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Frequently Asked Questions on HCF of 7309, 1709 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 7309, 1709?

Answer: HCF of 7309, 1709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7309, 1709 using Euclid's Algorithm?

Answer: For arbitrary numbers 7309, 1709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.