Highest Common Factor of 6514, 2571, 82137 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 6514, 2571, 82137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6514, 2571, 82137 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 6514, 2571, 82137 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 6514, 2571, 82137 is 1.

HCF(6514, 2571, 82137) = 1

HCF of 6514, 2571, 82137 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 6514, 2571, 82137 is 1.

Highest Common Factor of 6514,2571,82137 using Euclid's algorithm

Highest Common Factor of 6514,2571,82137 is 1

Step 1: Since 6514 > 2571, we apply the division lemma to 6514 and 2571, to get

6514 = 2571 x 2 + 1372

Step 2: Since the reminder 2571 ≠ 0, we apply division lemma to 1372 and 2571, to get

2571 = 1372 x 1 + 1199

Step 3: We consider the new divisor 1372 and the new remainder 1199, and apply the division lemma to get

1372 = 1199 x 1 + 173

We consider the new divisor 1199 and the new remainder 173,and apply the division lemma to get

1199 = 173 x 6 + 161

We consider the new divisor 173 and the new remainder 161,and apply the division lemma to get

173 = 161 x 1 + 12

We consider the new divisor 161 and the new remainder 12,and apply the division lemma to get

161 = 12 x 13 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 6514 and 2571 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(161,12) = HCF(173,161) = HCF(1199,173) = HCF(1372,1199) = HCF(2571,1372) = HCF(6514,2571) .

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

Step 1: Since 82137 > 1, we apply the division lemma to 82137 and 1, to get

82137 = 1 x 82137 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82137 is 1

Notice that 1 = HCF(82137,1) .

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Frequently Asked Questions on HCF of 6514, 2571, 82137 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 6514, 2571, 82137?

Answer: HCF of 6514, 2571, 82137 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6514, 2571, 82137 using Euclid's Algorithm?

Answer: For arbitrary numbers 6514, 2571, 82137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.