Highest Common Factor of 2027, 7669 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 2027, 7669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2027, 7669 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 2027, 7669 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 2027, 7669 is 1.

HCF(2027, 7669) = 1

HCF of 2027, 7669 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 2027, 7669 is 1.

Highest Common Factor of 2027,7669 using Euclid's algorithm

Highest Common Factor of 2027,7669 is 1

Step 1: Since 7669 > 2027, we apply the division lemma to 7669 and 2027, to get

7669 = 2027 x 3 + 1588

Step 2: Since the reminder 2027 ≠ 0, we apply division lemma to 1588 and 2027, to get

2027 = 1588 x 1 + 439

Step 3: We consider the new divisor 1588 and the new remainder 439, and apply the division lemma to get

1588 = 439 x 3 + 271

We consider the new divisor 439 and the new remainder 271,and apply the division lemma to get

439 = 271 x 1 + 168

We consider the new divisor 271 and the new remainder 168,and apply the division lemma to get

271 = 168 x 1 + 103

We consider the new divisor 168 and the new remainder 103,and apply the division lemma to get

168 = 103 x 1 + 65

We consider the new divisor 103 and the new remainder 65,and apply the division lemma to get

103 = 65 x 1 + 38

We consider the new divisor 65 and the new remainder 38,and apply the division lemma to get

65 = 38 x 1 + 27

We consider the new divisor 38 and the new remainder 27,and apply the division lemma to get

38 = 27 x 1 + 11

We consider the new divisor 27 and the new remainder 11,and apply the division lemma to get

27 = 11 x 2 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 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 2027 and 7669 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(38,27) = HCF(65,38) = HCF(103,65) = HCF(168,103) = HCF(271,168) = HCF(439,271) = HCF(1588,439) = HCF(2027,1588) = HCF(7669,2027) .

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Frequently Asked Questions on HCF of 2027, 7669 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 2027, 7669?

Answer: HCF of 2027, 7669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2027, 7669 using Euclid's Algorithm?

Answer: For arbitrary numbers 2027, 7669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.