Highest Common Factor of 2751, 8146 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 2751, 8146 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2751, 8146 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 2751, 8146 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 2751, 8146 is 1.

HCF(2751, 8146) = 1

HCF of 2751, 8146 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 2751, 8146 is 1.

Highest Common Factor of 2751,8146 using Euclid's algorithm

Highest Common Factor of 2751,8146 is 1

Step 1: Since 8146 > 2751, we apply the division lemma to 8146 and 2751, to get

8146 = 2751 x 2 + 2644

Step 2: Since the reminder 2751 ≠ 0, we apply division lemma to 2644 and 2751, to get

2751 = 2644 x 1 + 107

Step 3: We consider the new divisor 2644 and the new remainder 107, and apply the division lemma to get

2644 = 107 x 24 + 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 2751 and 8146 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(76,31) = HCF(107,76) = HCF(2644,107) = HCF(2751,2644) = HCF(8146,2751) .

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Frequently Asked Questions on HCF of 2751, 8146 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 2751, 8146?

Answer: HCF of 2751, 8146 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2751, 8146 using Euclid's Algorithm?

Answer: For arbitrary numbers 2751, 8146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.