Highest Common Factor of 758, 5034, 6109 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 758, 5034, 6109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 758, 5034, 6109 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 758, 5034, 6109 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 758, 5034, 6109 is 1.

HCF(758, 5034, 6109) = 1

HCF of 758, 5034, 6109 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 758, 5034, 6109 is 1.

Highest Common Factor of 758,5034,6109 using Euclid's algorithm

Highest Common Factor of 758,5034,6109 is 1

Step 1: Since 5034 > 758, we apply the division lemma to 5034 and 758, to get

5034 = 758 x 6 + 486

Step 2: Since the reminder 758 ≠ 0, we apply division lemma to 486 and 758, to get

758 = 486 x 1 + 272

Step 3: We consider the new divisor 486 and the new remainder 272, and apply the division lemma to get

486 = 272 x 1 + 214

We consider the new divisor 272 and the new remainder 214,and apply the division lemma to get

272 = 214 x 1 + 58

We consider the new divisor 214 and the new remainder 58,and apply the division lemma to get

214 = 58 x 3 + 40

We consider the new divisor 58 and the new remainder 40,and apply the division lemma to get

58 = 40 x 1 + 18

We consider the new divisor 40 and the new remainder 18,and apply the division lemma to get

40 = 18 x 2 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 758 and 5034 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(58,40) = HCF(214,58) = HCF(272,214) = HCF(486,272) = HCF(758,486) = HCF(5034,758) .

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

Step 1: Since 6109 > 2, we apply the division lemma to 6109 and 2, to get

6109 = 2 x 3054 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 6109 is 1

Notice that 1 = HCF(2,1) = HCF(6109,2) .

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Frequently Asked Questions on HCF of 758, 5034, 6109 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 758, 5034, 6109?

Answer: HCF of 758, 5034, 6109 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 758, 5034, 6109 using Euclid's Algorithm?

Answer: For arbitrary numbers 758, 5034, 6109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.