Highest Common Factor of 6780, 5403, 81892 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 6780, 5403, 81892 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6780, 5403, 81892 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 6780, 5403, 81892 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 6780, 5403, 81892 is 1.

HCF(6780, 5403, 81892) = 1

HCF of 6780, 5403, 81892 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 6780, 5403, 81892 is 1.

Highest Common Factor of 6780,5403,81892 using Euclid's algorithm

Highest Common Factor of 6780,5403,81892 is 1

Step 1: Since 6780 > 5403, we apply the division lemma to 6780 and 5403, to get

6780 = 5403 x 1 + 1377

Step 2: Since the reminder 5403 ≠ 0, we apply division lemma to 1377 and 5403, to get

5403 = 1377 x 3 + 1272

Step 3: We consider the new divisor 1377 and the new remainder 1272, and apply the division lemma to get

1377 = 1272 x 1 + 105

We consider the new divisor 1272 and the new remainder 105,and apply the division lemma to get

1272 = 105 x 12 + 12

We consider the new divisor 105 and the new remainder 12,and apply the division lemma to get

105 = 12 x 8 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6780 and 5403 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(105,12) = HCF(1272,105) = HCF(1377,1272) = HCF(5403,1377) = HCF(6780,5403) .

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

Step 1: Since 81892 > 3, we apply the division lemma to 81892 and 3, to get

81892 = 3 x 27297 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 81892 is 1

Notice that 1 = HCF(3,1) = HCF(81892,3) .

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Frequently Asked Questions on HCF of 6780, 5403, 81892 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 6780, 5403, 81892?

Answer: HCF of 6780, 5403, 81892 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6780, 5403, 81892 using Euclid's Algorithm?

Answer: For arbitrary numbers 6780, 5403, 81892 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.