Highest Common Factor of 3661, 6768 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 3661, 6768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3661, 6768 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 3661, 6768 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 3661, 6768 is 1.

HCF(3661, 6768) = 1

HCF of 3661, 6768 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 3661, 6768 is 1.

Highest Common Factor of 3661,6768 using Euclid's algorithm

Highest Common Factor of 3661,6768 is 1

Step 1: Since 6768 > 3661, we apply the division lemma to 6768 and 3661, to get

6768 = 3661 x 1 + 3107

Step 2: Since the reminder 3661 ≠ 0, we apply division lemma to 3107 and 3661, to get

3661 = 3107 x 1 + 554

Step 3: We consider the new divisor 3107 and the new remainder 554, and apply the division lemma to get

3107 = 554 x 5 + 337

We consider the new divisor 554 and the new remainder 337,and apply the division lemma to get

554 = 337 x 1 + 217

We consider the new divisor 337 and the new remainder 217,and apply the division lemma to get

337 = 217 x 1 + 120

We consider the new divisor 217 and the new remainder 120,and apply the division lemma to get

217 = 120 x 1 + 97

We consider the new divisor 120 and the new remainder 97,and apply the division lemma to get

120 = 97 x 1 + 23

We consider the new divisor 97 and the new remainder 23,and apply the division lemma to get

97 = 23 x 4 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 3661 and 6768 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(97,23) = HCF(120,97) = HCF(217,120) = HCF(337,217) = HCF(554,337) = HCF(3107,554) = HCF(3661,3107) = HCF(6768,3661) .

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Frequently Asked Questions on HCF of 3661, 6768 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 3661, 6768?

Answer: HCF of 3661, 6768 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3661, 6768 using Euclid's Algorithm?

Answer: For arbitrary numbers 3661, 6768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.