Highest Common Factor of 8666, 6123 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 8666, 6123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8666, 6123 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 8666, 6123 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 8666, 6123 is 1.

HCF(8666, 6123) = 1

HCF of 8666, 6123 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 8666, 6123 is 1.

Highest Common Factor of 8666,6123 using Euclid's algorithm

Highest Common Factor of 8666,6123 is 1

Step 1: Since 8666 > 6123, we apply the division lemma to 8666 and 6123, to get

8666 = 6123 x 1 + 2543

Step 2: Since the reminder 6123 ≠ 0, we apply division lemma to 2543 and 6123, to get

6123 = 2543 x 2 + 1037

Step 3: We consider the new divisor 2543 and the new remainder 1037, and apply the division lemma to get

2543 = 1037 x 2 + 469

We consider the new divisor 1037 and the new remainder 469,and apply the division lemma to get

1037 = 469 x 2 + 99

We consider the new divisor 469 and the new remainder 99,and apply the division lemma to get

469 = 99 x 4 + 73

We consider the new divisor 99 and the new remainder 73,and apply the division lemma to get

99 = 73 x 1 + 26

We consider the new divisor 73 and the new remainder 26,and apply the division lemma to get

73 = 26 x 2 + 21

We consider the new divisor 26 and the new remainder 21,and apply the division lemma to get

26 = 21 x 1 + 5

We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get

21 = 5 x 4 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8666 and 6123 is 1

Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(26,21) = HCF(73,26) = HCF(99,73) = HCF(469,99) = HCF(1037,469) = HCF(2543,1037) = HCF(6123,2543) = HCF(8666,6123) .

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Frequently Asked Questions on HCF of 8666, 6123 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 8666, 6123?

Answer: HCF of 8666, 6123 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8666, 6123 using Euclid's Algorithm?

Answer: For arbitrary numbers 8666, 6123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.