Highest Common Factor of 768, 884, 866 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 768, 884, 866 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 768, 884, 866 is 2 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 768, 884, 866 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 768, 884, 866 is 2.

HCF(768, 884, 866) = 2

HCF of 768, 884, 866 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 768, 884, 866 is 2.

Highest Common Factor of 768,884,866 using Euclid's algorithm

Highest Common Factor of 768,884,866 is 2

Step 1: Since 884 > 768, we apply the division lemma to 884 and 768, to get

884 = 768 x 1 + 116

Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 116 and 768, to get

768 = 116 x 6 + 72

Step 3: We consider the new divisor 116 and the new remainder 72, and apply the division lemma to get

116 = 72 x 1 + 44

We consider the new divisor 72 and the new remainder 44,and apply the division lemma to get

72 = 44 x 1 + 28

We consider the new divisor 44 and the new remainder 28,and apply the division lemma to get

44 = 28 x 1 + 16

We consider the new divisor 28 and the new remainder 16,and apply the division lemma to get

28 = 16 x 1 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 768 and 884 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(28,16) = HCF(44,28) = HCF(72,44) = HCF(116,72) = HCF(768,116) = HCF(884,768) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 866 > 4, we apply the division lemma to 866 and 4, to get

866 = 4 x 216 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 866 is 2

Notice that 2 = HCF(4,2) = HCF(866,4) .

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Frequently Asked Questions on HCF of 768, 884, 866 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 768, 884, 866?

Answer: HCF of 768, 884, 866 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 768, 884, 866 using Euclid's Algorithm?

Answer: For arbitrary numbers 768, 884, 866 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.