Highest Common Factor of 6105, 2810, 18739 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 6105, 2810, 18739 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6105, 2810, 18739 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 6105, 2810, 18739 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 6105, 2810, 18739 is 1.

HCF(6105, 2810, 18739) = 1

HCF of 6105, 2810, 18739 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 6105, 2810, 18739 is 1.

Highest Common Factor of 6105,2810,18739 using Euclid's algorithm

Highest Common Factor of 6105,2810,18739 is 1

Step 1: Since 6105 > 2810, we apply the division lemma to 6105 and 2810, to get

6105 = 2810 x 2 + 485

Step 2: Since the reminder 2810 ≠ 0, we apply division lemma to 485 and 2810, to get

2810 = 485 x 5 + 385

Step 3: We consider the new divisor 485 and the new remainder 385, and apply the division lemma to get

485 = 385 x 1 + 100

We consider the new divisor 385 and the new remainder 100,and apply the division lemma to get

385 = 100 x 3 + 85

We consider the new divisor 100 and the new remainder 85,and apply the division lemma to get

100 = 85 x 1 + 15

We consider the new divisor 85 and the new remainder 15,and apply the division lemma to get

85 = 15 x 5 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6105 and 2810 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(85,15) = HCF(100,85) = HCF(385,100) = HCF(485,385) = HCF(2810,485) = HCF(6105,2810) .

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

Step 1: Since 18739 > 5, we apply the division lemma to 18739 and 5, to get

18739 = 5 x 3747 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 18739 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(18739,5) .

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Frequently Asked Questions on HCF of 6105, 2810, 18739 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 6105, 2810, 18739?

Answer: HCF of 6105, 2810, 18739 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6105, 2810, 18739 using Euclid's Algorithm?

Answer: For arbitrary numbers 6105, 2810, 18739 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.