Highest Common Factor of 586, 364, 283 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, 364, 283 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 364, 283 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, 364, 283 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, 364, 283 is 1.

HCF(586, 364, 283) = 1

HCF of 586, 364, 283 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, 364, 283 is 1.

Highest Common Factor of 586,364,283 using Euclid's algorithm

Highest Common Factor of 586,364,283 is 1

Step 1: Since 586 > 364, we apply the division lemma to 586 and 364, to get

586 = 364 x 1 + 222

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 222 and 364, to get

364 = 222 x 1 + 142

Step 3: We consider the new divisor 222 and the new remainder 142, and apply the division lemma to get

222 = 142 x 1 + 80

We consider the new divisor 142 and the new remainder 80,and apply the division lemma to get

142 = 80 x 1 + 62

We consider the new divisor 80 and the new remainder 62,and apply the division lemma to get

80 = 62 x 1 + 18

We consider the new divisor 62 and the new remainder 18,and apply the division lemma to get

62 = 18 x 3 + 8

We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get

18 = 8 x 2 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 586 and 364 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(62,18) = HCF(80,62) = HCF(142,80) = HCF(222,142) = HCF(364,222) = HCF(586,364) .

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

Step 1: Since 283 > 2, we apply the division lemma to 283 and 2, to get

283 = 2 x 141 + 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 283 is 1

Notice that 1 = HCF(2,1) = HCF(283,2) .

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Frequently Asked Questions on HCF of 586, 364, 283 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, 364, 283?

Answer: HCF of 586, 364, 283 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 364, 283 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 364, 283 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.