Highest Common Factor of 867, 681, 682 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 867, 681, 682 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 681, 682 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 867, 681, 682 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 867, 681, 682 is 1.

HCF(867, 681, 682) = 1

HCF of 867, 681, 682 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 867, 681, 682 is 1.

Highest Common Factor of 867,681,682 using Euclid's algorithm

Highest Common Factor of 867,681,682 is 1

Step 1: Since 867 > 681, we apply the division lemma to 867 and 681, to get

867 = 681 x 1 + 186

Step 2: Since the reminder 681 ≠ 0, we apply division lemma to 186 and 681, to get

681 = 186 x 3 + 123

Step 3: We consider the new divisor 186 and the new remainder 123, and apply the division lemma to get

186 = 123 x 1 + 63

We consider the new divisor 123 and the new remainder 63,and apply the division lemma to get

123 = 63 x 1 + 60

We consider the new divisor 63 and the new remainder 60,and apply the division lemma to get

63 = 60 x 1 + 3

We consider the new divisor 60 and the new remainder 3,and apply the division lemma to get

60 = 3 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 681 is 3

Notice that 3 = HCF(60,3) = HCF(63,60) = HCF(123,63) = HCF(186,123) = HCF(681,186) = HCF(867,681) .

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

Step 1: Since 682 > 3, we apply the division lemma to 682 and 3, to get

682 = 3 x 227 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 682 is 1

Notice that 1 = HCF(3,1) = HCF(682,3) .

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Frequently Asked Questions on HCF of 867, 681, 682 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 867, 681, 682?

Answer: HCF of 867, 681, 682 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 681, 682 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 681, 682 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.