Highest Common Factor of 806, 320, 677 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, 320, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 806, 320, 677 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, 320, 677 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, 320, 677 is 1.

HCF(806, 320, 677) = 1

HCF of 806, 320, 677 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, 320, 677 is 1.

Highest Common Factor of 806,320,677 using Euclid's algorithm

Highest Common Factor of 806,320,677 is 1

Step 1: Since 806 > 320, we apply the division lemma to 806 and 320, to get

806 = 320 x 2 + 166

Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 166 and 320, to get

320 = 166 x 1 + 154

Step 3: We consider the new divisor 166 and the new remainder 154, and apply the division lemma to get

166 = 154 x 1 + 12

We consider the new divisor 154 and the new remainder 12,and apply the division lemma to get

154 = 12 x 12 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 806 and 320 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(154,12) = HCF(166,154) = HCF(320,166) = HCF(806,320) .

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

Step 1: Since 677 > 2, we apply the division lemma to 677 and 2, to get

677 = 2 x 338 + 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 677 is 1

Notice that 1 = HCF(2,1) = HCF(677,2) .

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Frequently Asked Questions on HCF of 806, 320, 677 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, 320, 677?

Answer: HCF of 806, 320, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 806, 320, 677 using Euclid's Algorithm?

Answer: For arbitrary numbers 806, 320, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.