Highest Common Factor of 8027, 6609 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 8027, 6609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8027, 6609 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 8027, 6609 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 8027, 6609 is 1.

HCF(8027, 6609) = 1

HCF of 8027, 6609 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 8027, 6609 is 1.

Highest Common Factor of 8027,6609 using Euclid's algorithm

Highest Common Factor of 8027,6609 is 1

Step 1: Since 8027 > 6609, we apply the division lemma to 8027 and 6609, to get

8027 = 6609 x 1 + 1418

Step 2: Since the reminder 6609 ≠ 0, we apply division lemma to 1418 and 6609, to get

6609 = 1418 x 4 + 937

Step 3: We consider the new divisor 1418 and the new remainder 937, and apply the division lemma to get

1418 = 937 x 1 + 481

We consider the new divisor 937 and the new remainder 481,and apply the division lemma to get

937 = 481 x 1 + 456

We consider the new divisor 481 and the new remainder 456,and apply the division lemma to get

481 = 456 x 1 + 25

We consider the new divisor 456 and the new remainder 25,and apply the division lemma to get

456 = 25 x 18 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8027 and 6609 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(456,25) = HCF(481,456) = HCF(937,481) = HCF(1418,937) = HCF(6609,1418) = HCF(8027,6609) .

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Frequently Asked Questions on HCF of 8027, 6609 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 8027, 6609?

Answer: HCF of 8027, 6609 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8027, 6609 using Euclid's Algorithm?

Answer: For arbitrary numbers 8027, 6609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.