Highest Common Factor of 6903, 3856, 17760 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 6903, 3856, 17760 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6903, 3856, 17760 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 6903, 3856, 17760 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 6903, 3856, 17760 is 1.

HCF(6903, 3856, 17760) = 1

HCF of 6903, 3856, 17760 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 6903, 3856, 17760 is 1.

Highest Common Factor of 6903,3856,17760 using Euclid's algorithm

Highest Common Factor of 6903,3856,17760 is 1

Step 1: Since 6903 > 3856, we apply the division lemma to 6903 and 3856, to get

6903 = 3856 x 1 + 3047

Step 2: Since the reminder 3856 ≠ 0, we apply division lemma to 3047 and 3856, to get

3856 = 3047 x 1 + 809

Step 3: We consider the new divisor 3047 and the new remainder 809, and apply the division lemma to get

3047 = 809 x 3 + 620

We consider the new divisor 809 and the new remainder 620,and apply the division lemma to get

809 = 620 x 1 + 189

We consider the new divisor 620 and the new remainder 189,and apply the division lemma to get

620 = 189 x 3 + 53

We consider the new divisor 189 and the new remainder 53,and apply the division lemma to get

189 = 53 x 3 + 30

We consider the new divisor 53 and the new remainder 30,and apply the division lemma to get

53 = 30 x 1 + 23

We consider the new divisor 30 and the new remainder 23,and apply the division lemma to get

30 = 23 x 1 + 7

We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get

23 = 7 x 3 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 6903 and 3856 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(53,30) = HCF(189,53) = HCF(620,189) = HCF(809,620) = HCF(3047,809) = HCF(3856,3047) = HCF(6903,3856) .

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

Step 1: Since 17760 > 1, we apply the division lemma to 17760 and 1, to get

17760 = 1 x 17760 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 17760 is 1

Notice that 1 = HCF(17760,1) .

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Frequently Asked Questions on HCF of 6903, 3856, 17760 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 6903, 3856, 17760?

Answer: HCF of 6903, 3856, 17760 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6903, 3856, 17760 using Euclid's Algorithm?

Answer: For arbitrary numbers 6903, 3856, 17760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.