Highest Common Factor of 6078, 8625, 43408 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 6078, 8625, 43408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6078, 8625, 43408 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 6078, 8625, 43408 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 6078, 8625, 43408 is 1.

HCF(6078, 8625, 43408) = 1

HCF of 6078, 8625, 43408 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 6078, 8625, 43408 is 1.

Highest Common Factor of 6078,8625,43408 using Euclid's algorithm

Highest Common Factor of 6078,8625,43408 is 1

Step 1: Since 8625 > 6078, we apply the division lemma to 8625 and 6078, to get

8625 = 6078 x 1 + 2547

Step 2: Since the reminder 6078 ≠ 0, we apply division lemma to 2547 and 6078, to get

6078 = 2547 x 2 + 984

Step 3: We consider the new divisor 2547 and the new remainder 984, and apply the division lemma to get

2547 = 984 x 2 + 579

We consider the new divisor 984 and the new remainder 579,and apply the division lemma to get

984 = 579 x 1 + 405

We consider the new divisor 579 and the new remainder 405,and apply the division lemma to get

579 = 405 x 1 + 174

We consider the new divisor 405 and the new remainder 174,and apply the division lemma to get

405 = 174 x 2 + 57

We consider the new divisor 174 and the new remainder 57,and apply the division lemma to get

174 = 57 x 3 + 3

We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get

57 = 3 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6078 and 8625 is 3

Notice that 3 = HCF(57,3) = HCF(174,57) = HCF(405,174) = HCF(579,405) = HCF(984,579) = HCF(2547,984) = HCF(6078,2547) = HCF(8625,6078) .

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

Step 1: Since 43408 > 3, we apply the division lemma to 43408 and 3, to get

43408 = 3 x 14469 + 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 43408 is 1

Notice that 1 = HCF(3,1) = HCF(43408,3) .

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Frequently Asked Questions on HCF of 6078, 8625, 43408 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 6078, 8625, 43408?

Answer: HCF of 6078, 8625, 43408 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6078, 8625, 43408 using Euclid's Algorithm?

Answer: For arbitrary numbers 6078, 8625, 43408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.