Highest Common Factor of 2017, 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 2017, 1709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2017, 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 2017, 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 2017, 1709 is 1.

HCF(2017, 1709) = 1

HCF of 2017, 1709 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 2017, 1709 is 1.

Highest Common Factor of 2017,1709 using Euclid's algorithm

Highest Common Factor of 2017,1709 is 1

Step 1: Since 2017 > 1709, we apply the division lemma to 2017 and 1709, to get

2017 = 1709 x 1 + 308

Step 2: Since the reminder 1709 ≠ 0, we apply division lemma to 308 and 1709, to get

1709 = 308 x 5 + 169

Step 3: We consider the new divisor 308 and the new remainder 169, and apply the division lemma to get

308 = 169 x 1 + 139

We consider the new divisor 169 and the new remainder 139,and apply the division lemma to get

169 = 139 x 1 + 30

We consider the new divisor 139 and the new remainder 30,and apply the division lemma to get

139 = 30 x 4 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 2017 and 1709 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(139,30) = HCF(169,139) = HCF(308,169) = HCF(1709,308) = HCF(2017,1709) .

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Frequently Asked Questions on HCF of 2017, 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 2017, 1709?

Answer: HCF of 2017, 1709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2017, 1709 using Euclid's Algorithm?

Answer: For arbitrary numbers 2017, 1709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.