Highest Common Factor of 586, 7403, 8734 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 586, 7403, 8734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 7403, 8734 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 586, 7403, 8734 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 586, 7403, 8734 is 1.

HCF(586, 7403, 8734) = 1

HCF of 586, 7403, 8734 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 586, 7403, 8734 is 1.

Highest Common Factor of 586,7403,8734 using Euclid's algorithm

Highest Common Factor of 586,7403,8734 is 1

Step 1: Since 7403 > 586, we apply the division lemma to 7403 and 586, to get

7403 = 586 x 12 + 371

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 371 and 586, to get

586 = 371 x 1 + 215

Step 3: We consider the new divisor 371 and the new remainder 215, and apply the division lemma to get

371 = 215 x 1 + 156

We consider the new divisor 215 and the new remainder 156,and apply the division lemma to get

215 = 156 x 1 + 59

We consider the new divisor 156 and the new remainder 59,and apply the division lemma to get

156 = 59 x 2 + 38

We consider the new divisor 59 and the new remainder 38,and apply the division lemma to get

59 = 38 x 1 + 21

We consider the new divisor 38 and the new remainder 21,and apply the division lemma to get

38 = 21 x 1 + 17

We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get

21 = 17 x 1 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 586 and 7403 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(38,21) = HCF(59,38) = HCF(156,59) = HCF(215,156) = HCF(371,215) = HCF(586,371) = HCF(7403,586) .

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

Step 1: Since 8734 > 1, we apply the division lemma to 8734 and 1, to get

8734 = 1 x 8734 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8734 is 1

Notice that 1 = HCF(8734,1) .

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Frequently Asked Questions on HCF of 586, 7403, 8734 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 586, 7403, 8734?

Answer: HCF of 586, 7403, 8734 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 7403, 8734 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 7403, 8734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.