Highest Common Factor of 6209, 8361, 37918 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 6209, 8361, 37918 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6209, 8361, 37918 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 6209, 8361, 37918 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 6209, 8361, 37918 is 1.

HCF(6209, 8361, 37918) = 1

HCF of 6209, 8361, 37918 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 6209, 8361, 37918 is 1.

Highest Common Factor of 6209,8361,37918 using Euclid's algorithm

Highest Common Factor of 6209,8361,37918 is 1

Step 1: Since 8361 > 6209, we apply the division lemma to 8361 and 6209, to get

8361 = 6209 x 1 + 2152

Step 2: Since the reminder 6209 ≠ 0, we apply division lemma to 2152 and 6209, to get

6209 = 2152 x 2 + 1905

Step 3: We consider the new divisor 2152 and the new remainder 1905, and apply the division lemma to get

2152 = 1905 x 1 + 247

We consider the new divisor 1905 and the new remainder 247,and apply the division lemma to get

1905 = 247 x 7 + 176

We consider the new divisor 247 and the new remainder 176,and apply the division lemma to get

247 = 176 x 1 + 71

We consider the new divisor 176 and the new remainder 71,and apply the division lemma to get

176 = 71 x 2 + 34

We consider the new divisor 71 and the new remainder 34,and apply the division lemma to get

71 = 34 x 2 + 3

We consider the new divisor 34 and the new remainder 3,and apply the division lemma to get

34 = 3 x 11 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6209 and 8361 is 1

Notice that 1 = HCF(3,1) = HCF(34,3) = HCF(71,34) = HCF(176,71) = HCF(247,176) = HCF(1905,247) = HCF(2152,1905) = HCF(6209,2152) = HCF(8361,6209) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 37918 > 1, we apply the division lemma to 37918 and 1, to get

37918 = 1 x 37918 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37918 is 1

Notice that 1 = HCF(37918,1) .

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Frequently Asked Questions on HCF of 6209, 8361, 37918 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 6209, 8361, 37918?

Answer: HCF of 6209, 8361, 37918 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6209, 8361, 37918 using Euclid's Algorithm?

Answer: For arbitrary numbers 6209, 8361, 37918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.