Highest Common Factor of 1012, 6812 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 1012, 6812 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 1012, 6812 is 4 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 1012, 6812 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 1012, 6812 is 4.

HCF(1012, 6812) = 4

HCF of 1012, 6812 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 1012, 6812 is 4.

Highest Common Factor of 1012,6812 using Euclid's algorithm

Highest Common Factor of 1012,6812 is 4

Step 1: Since 6812 > 1012, we apply the division lemma to 6812 and 1012, to get

6812 = 1012 x 6 + 740

Step 2: Since the reminder 1012 ≠ 0, we apply division lemma to 740 and 1012, to get

1012 = 740 x 1 + 272

Step 3: We consider the new divisor 740 and the new remainder 272, and apply the division lemma to get

740 = 272 x 2 + 196

We consider the new divisor 272 and the new remainder 196,and apply the division lemma to get

272 = 196 x 1 + 76

We consider the new divisor 196 and the new remainder 76,and apply the division lemma to get

196 = 76 x 2 + 44

We consider the new divisor 76 and the new remainder 44,and apply the division lemma to get

76 = 44 x 1 + 32

We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get

44 = 32 x 1 + 12

We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get

32 = 12 x 2 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 1012 and 6812 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(76,44) = HCF(196,76) = HCF(272,196) = HCF(740,272) = HCF(1012,740) = HCF(6812,1012) .

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Frequently Asked Questions on HCF of 1012, 6812 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 1012, 6812?

Answer: HCF of 1012, 6812 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1012, 6812 using Euclid's Algorithm?

Answer: For arbitrary numbers 1012, 6812 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.