Highest Common Factor of 2005, 6737 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 2005, 6737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2005, 6737 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 2005, 6737 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 2005, 6737 is 1.

HCF(2005, 6737) = 1

HCF of 2005, 6737 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 2005, 6737 is 1.

Highest Common Factor of 2005,6737 using Euclid's algorithm

Highest Common Factor of 2005,6737 is 1

Step 1: Since 6737 > 2005, we apply the division lemma to 6737 and 2005, to get

6737 = 2005 x 3 + 722

Step 2: Since the reminder 2005 ≠ 0, we apply division lemma to 722 and 2005, to get

2005 = 722 x 2 + 561

Step 3: We consider the new divisor 722 and the new remainder 561, and apply the division lemma to get

722 = 561 x 1 + 161

We consider the new divisor 561 and the new remainder 161,and apply the division lemma to get

561 = 161 x 3 + 78

We consider the new divisor 161 and the new remainder 78,and apply the division lemma to get

161 = 78 x 2 + 5

We consider the new divisor 78 and the new remainder 5,and apply the division lemma to get

78 = 5 x 15 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 2005 and 6737 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(78,5) = HCF(161,78) = HCF(561,161) = HCF(722,561) = HCF(2005,722) = HCF(6737,2005) .

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Frequently Asked Questions on HCF of 2005, 6737 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 2005, 6737?

Answer: HCF of 2005, 6737 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2005, 6737 using Euclid's Algorithm?

Answer: For arbitrary numbers 2005, 6737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.