Highest Common Factor of 6739, 5678, 82722 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 6739, 5678, 82722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6739, 5678, 82722 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 6739, 5678, 82722 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 6739, 5678, 82722 is 1.

HCF(6739, 5678, 82722) = 1

HCF of 6739, 5678, 82722 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 6739, 5678, 82722 is 1.

Highest Common Factor of 6739,5678,82722 using Euclid's algorithm

Highest Common Factor of 6739,5678,82722 is 1

Step 1: Since 6739 > 5678, we apply the division lemma to 6739 and 5678, to get

6739 = 5678 x 1 + 1061

Step 2: Since the reminder 5678 ≠ 0, we apply division lemma to 1061 and 5678, to get

5678 = 1061 x 5 + 373

Step 3: We consider the new divisor 1061 and the new remainder 373, and apply the division lemma to get

1061 = 373 x 2 + 315

We consider the new divisor 373 and the new remainder 315,and apply the division lemma to get

373 = 315 x 1 + 58

We consider the new divisor 315 and the new remainder 58,and apply the division lemma to get

315 = 58 x 5 + 25

We consider the new divisor 58 and the new remainder 25,and apply the division lemma to get

58 = 25 x 2 + 8

We consider the new divisor 25 and the new remainder 8,and apply the division lemma to get

25 = 8 x 3 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6739 and 5678 is 1

Notice that 1 = HCF(8,1) = HCF(25,8) = HCF(58,25) = HCF(315,58) = HCF(373,315) = HCF(1061,373) = HCF(5678,1061) = HCF(6739,5678) .

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

Step 1: Since 82722 > 1, we apply the division lemma to 82722 and 1, to get

82722 = 1 x 82722 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82722 is 1

Notice that 1 = HCF(82722,1) .

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Frequently Asked Questions on HCF of 6739, 5678, 82722 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 6739, 5678, 82722?

Answer: HCF of 6739, 5678, 82722 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6739, 5678, 82722 using Euclid's Algorithm?

Answer: For arbitrary numbers 6739, 5678, 82722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.