Highest Common Factor of 2783, 6706 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 2783, 6706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2783, 6706 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 2783, 6706 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 2783, 6706 is 1.

HCF(2783, 6706) = 1

HCF of 2783, 6706 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 2783, 6706 is 1.

Highest Common Factor of 2783,6706 using Euclid's algorithm

Highest Common Factor of 2783,6706 is 1

Step 1: Since 6706 > 2783, we apply the division lemma to 6706 and 2783, to get

6706 = 2783 x 2 + 1140

Step 2: Since the reminder 2783 ≠ 0, we apply division lemma to 1140 and 2783, to get

2783 = 1140 x 2 + 503

Step 3: We consider the new divisor 1140 and the new remainder 503, and apply the division lemma to get

1140 = 503 x 2 + 134

We consider the new divisor 503 and the new remainder 134,and apply the division lemma to get

503 = 134 x 3 + 101

We consider the new divisor 134 and the new remainder 101,and apply the division lemma to get

134 = 101 x 1 + 33

We consider the new divisor 101 and the new remainder 33,and apply the division lemma to get

101 = 33 x 3 + 2

We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get

33 = 2 x 16 + 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 2783 and 6706 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(101,33) = HCF(134,101) = HCF(503,134) = HCF(1140,503) = HCF(2783,1140) = HCF(6706,2783) .

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Frequently Asked Questions on HCF of 2783, 6706 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 2783, 6706?

Answer: HCF of 2783, 6706 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2783, 6706 using Euclid's Algorithm?

Answer: For arbitrary numbers 2783, 6706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.