Highest Common Factor of 806, 684, 61 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 806, 684, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 806, 684, 61 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 806, 684, 61 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 806, 684, 61 is 1.

HCF(806, 684, 61) = 1

HCF of 806, 684, 61 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 806, 684, 61 is 1.

Highest Common Factor of 806,684,61 using Euclid's algorithm

Highest Common Factor of 806,684,61 is 1

Step 1: Since 806 > 684, we apply the division lemma to 806 and 684, to get

806 = 684 x 1 + 122

Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 122 and 684, to get

684 = 122 x 5 + 74

Step 3: We consider the new divisor 122 and the new remainder 74, and apply the division lemma to get

122 = 74 x 1 + 48

We consider the new divisor 74 and the new remainder 48,and apply the division lemma to get

74 = 48 x 1 + 26

We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get

48 = 26 x 1 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 806 and 684 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(74,48) = HCF(122,74) = HCF(684,122) = HCF(806,684) .

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

Step 1: Since 61 > 2, we apply the division lemma to 61 and 2, to get

61 = 2 x 30 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 61 is 1

Notice that 1 = HCF(2,1) = HCF(61,2) .

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Frequently Asked Questions on HCF of 806, 684, 61 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 806, 684, 61?

Answer: HCF of 806, 684, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 806, 684, 61 using Euclid's Algorithm?

Answer: For arbitrary numbers 806, 684, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.