Highest Common Factor of 6881, 1909, 37130 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 6881, 1909, 37130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6881, 1909, 37130 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 6881, 1909, 37130 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 6881, 1909, 37130 is 1.

HCF(6881, 1909, 37130) = 1

HCF of 6881, 1909, 37130 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 6881, 1909, 37130 is 1.

Highest Common Factor of 6881,1909,37130 using Euclid's algorithm

Highest Common Factor of 6881,1909,37130 is 1

Step 1: Since 6881 > 1909, we apply the division lemma to 6881 and 1909, to get

6881 = 1909 x 3 + 1154

Step 2: Since the reminder 1909 ≠ 0, we apply division lemma to 1154 and 1909, to get

1909 = 1154 x 1 + 755

Step 3: We consider the new divisor 1154 and the new remainder 755, and apply the division lemma to get

1154 = 755 x 1 + 399

We consider the new divisor 755 and the new remainder 399,and apply the division lemma to get

755 = 399 x 1 + 356

We consider the new divisor 399 and the new remainder 356,and apply the division lemma to get

399 = 356 x 1 + 43

We consider the new divisor 356 and the new remainder 43,and apply the division lemma to get

356 = 43 x 8 + 12

We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get

43 = 12 x 3 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 6881 and 1909 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(356,43) = HCF(399,356) = HCF(755,399) = HCF(1154,755) = HCF(1909,1154) = HCF(6881,1909) .

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

Step 1: Since 37130 > 1, we apply the division lemma to 37130 and 1, to get

37130 = 1 x 37130 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37130 is 1

Notice that 1 = HCF(37130,1) .

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Frequently Asked Questions on HCF of 6881, 1909, 37130 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 6881, 1909, 37130?

Answer: HCF of 6881, 1909, 37130 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6881, 1909, 37130 using Euclid's Algorithm?

Answer: For arbitrary numbers 6881, 1909, 37130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.