Highest Common Factor of 677, 6011, 8735 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 677, 6011, 8735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 6011, 8735 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 677, 6011, 8735 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 677, 6011, 8735 is 1.

HCF(677, 6011, 8735) = 1

HCF of 677, 6011, 8735 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 677, 6011, 8735 is 1.

Highest Common Factor of 677,6011,8735 using Euclid's algorithm

Highest Common Factor of 677,6011,8735 is 1

Step 1: Since 6011 > 677, we apply the division lemma to 6011 and 677, to get

6011 = 677 x 8 + 595

Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 595 and 677, to get

677 = 595 x 1 + 82

Step 3: We consider the new divisor 595 and the new remainder 82, and apply the division lemma to get

595 = 82 x 7 + 21

We consider the new divisor 82 and the new remainder 21,and apply the division lemma to get

82 = 21 x 3 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 677 and 6011 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(82,21) = HCF(595,82) = HCF(677,595) = HCF(6011,677) .

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

Step 1: Since 8735 > 1, we apply the division lemma to 8735 and 1, to get

8735 = 1 x 8735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8735 is 1

Notice that 1 = HCF(8735,1) .

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Frequently Asked Questions on HCF of 677, 6011, 8735 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 677, 6011, 8735?

Answer: HCF of 677, 6011, 8735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 6011, 8735 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 6011, 8735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.