Highest Common Factor of 6977, 8657 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 6977, 8657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6977, 8657 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 6977, 8657 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 6977, 8657 is 1.

HCF(6977, 8657) = 1

HCF of 6977, 8657 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 6977, 8657 is 1.

Highest Common Factor of 6977,8657 using Euclid's algorithm

Highest Common Factor of 6977,8657 is 1

Step 1: Since 8657 > 6977, we apply the division lemma to 8657 and 6977, to get

8657 = 6977 x 1 + 1680

Step 2: Since the reminder 6977 ≠ 0, we apply division lemma to 1680 and 6977, to get

6977 = 1680 x 4 + 257

Step 3: We consider the new divisor 1680 and the new remainder 257, and apply the division lemma to get

1680 = 257 x 6 + 138

We consider the new divisor 257 and the new remainder 138,and apply the division lemma to get

257 = 138 x 1 + 119

We consider the new divisor 138 and the new remainder 119,and apply the division lemma to get

138 = 119 x 1 + 19

We consider the new divisor 119 and the new remainder 19,and apply the division lemma to get

119 = 19 x 6 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6977 and 8657 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(119,19) = HCF(138,119) = HCF(257,138) = HCF(1680,257) = HCF(6977,1680) = HCF(8657,6977) .

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Frequently Asked Questions on HCF of 6977, 8657 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 6977, 8657?

Answer: HCF of 6977, 8657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6977, 8657 using Euclid's Algorithm?

Answer: For arbitrary numbers 6977, 8657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.