Highest Common Factor of 3687, 6344 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 3687, 6344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3687, 6344 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 3687, 6344 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 3687, 6344 is 1.

HCF(3687, 6344) = 1

HCF of 3687, 6344 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 3687, 6344 is 1.

Highest Common Factor of 3687,6344 using Euclid's algorithm

Highest Common Factor of 3687,6344 is 1

Step 1: Since 6344 > 3687, we apply the division lemma to 6344 and 3687, to get

6344 = 3687 x 1 + 2657

Step 2: Since the reminder 3687 ≠ 0, we apply division lemma to 2657 and 3687, to get

3687 = 2657 x 1 + 1030

Step 3: We consider the new divisor 2657 and the new remainder 1030, and apply the division lemma to get

2657 = 1030 x 2 + 597

We consider the new divisor 1030 and the new remainder 597,and apply the division lemma to get

1030 = 597 x 1 + 433

We consider the new divisor 597 and the new remainder 433,and apply the division lemma to get

597 = 433 x 1 + 164

We consider the new divisor 433 and the new remainder 164,and apply the division lemma to get

433 = 164 x 2 + 105

We consider the new divisor 164 and the new remainder 105,and apply the division lemma to get

164 = 105 x 1 + 59

We consider the new divisor 105 and the new remainder 59,and apply the division lemma to get

105 = 59 x 1 + 46

We consider the new divisor 59 and the new remainder 46,and apply the division lemma to get

59 = 46 x 1 + 13

We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get

46 = 13 x 3 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 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 3687 and 6344 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(105,59) = HCF(164,105) = HCF(433,164) = HCF(597,433) = HCF(1030,597) = HCF(2657,1030) = HCF(3687,2657) = HCF(6344,3687) .

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Frequently Asked Questions on HCF of 3687, 6344 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 3687, 6344?

Answer: HCF of 3687, 6344 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3687, 6344 using Euclid's Algorithm?

Answer: For arbitrary numbers 3687, 6344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.