Highest Common Factor of 6908, 2051 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 6908, 2051 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6908, 2051 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 6908, 2051 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 6908, 2051 is 1.

HCF(6908, 2051) = 1

HCF of 6908, 2051 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 6908, 2051 is 1.

Highest Common Factor of 6908,2051 using Euclid's algorithm

Highest Common Factor of 6908,2051 is 1

Step 1: Since 6908 > 2051, we apply the division lemma to 6908 and 2051, to get

6908 = 2051 x 3 + 755

Step 2: Since the reminder 2051 ≠ 0, we apply division lemma to 755 and 2051, to get

2051 = 755 x 2 + 541

Step 3: We consider the new divisor 755 and the new remainder 541, and apply the division lemma to get

755 = 541 x 1 + 214

We consider the new divisor 541 and the new remainder 214,and apply the division lemma to get

541 = 214 x 2 + 113

We consider the new divisor 214 and the new remainder 113,and apply the division lemma to get

214 = 113 x 1 + 101

We consider the new divisor 113 and the new remainder 101,and apply the division lemma to get

113 = 101 x 1 + 12

We consider the new divisor 101 and the new remainder 12,and apply the division lemma to get

101 = 12 x 8 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 6908 and 2051 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(101,12) = HCF(113,101) = HCF(214,113) = HCF(541,214) = HCF(755,541) = HCF(2051,755) = HCF(6908,2051) .

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Frequently Asked Questions on HCF of 6908, 2051 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 6908, 2051?

Answer: HCF of 6908, 2051 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6908, 2051 using Euclid's Algorithm?

Answer: For arbitrary numbers 6908, 2051 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.