Highest Common Factor of 2617, 6697 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 2617, 6697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2617, 6697 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 2617, 6697 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 2617, 6697 is 1.

HCF(2617, 6697) = 1

HCF of 2617, 6697 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 2617, 6697 is 1.

Highest Common Factor of 2617,6697 using Euclid's algorithm

Highest Common Factor of 2617,6697 is 1

Step 1: Since 6697 > 2617, we apply the division lemma to 6697 and 2617, to get

6697 = 2617 x 2 + 1463

Step 2: Since the reminder 2617 ≠ 0, we apply division lemma to 1463 and 2617, to get

2617 = 1463 x 1 + 1154

Step 3: We consider the new divisor 1463 and the new remainder 1154, and apply the division lemma to get

1463 = 1154 x 1 + 309

We consider the new divisor 1154 and the new remainder 309,and apply the division lemma to get

1154 = 309 x 3 + 227

We consider the new divisor 309 and the new remainder 227,and apply the division lemma to get

309 = 227 x 1 + 82

We consider the new divisor 227 and the new remainder 82,and apply the division lemma to get

227 = 82 x 2 + 63

We consider the new divisor 82 and the new remainder 63,and apply the division lemma to get

82 = 63 x 1 + 19

We consider the new divisor 63 and the new remainder 19,and apply the division lemma to get

63 = 19 x 3 + 6

We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get

19 = 6 x 3 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2617 and 6697 is 1

Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(63,19) = HCF(82,63) = HCF(227,82) = HCF(309,227) = HCF(1154,309) = HCF(1463,1154) = HCF(2617,1463) = HCF(6697,2617) .

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Frequently Asked Questions on HCF of 2617, 6697 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 2617, 6697?

Answer: HCF of 2617, 6697 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2617, 6697 using Euclid's Algorithm?

Answer: For arbitrary numbers 2617, 6697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.