Highest Common Factor of 586, 175, 529 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, 175, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 175, 529 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, 175, 529 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, 175, 529 is 1.

HCF(586, 175, 529) = 1

HCF of 586, 175, 529 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, 175, 529 is 1.

Highest Common Factor of 586,175,529 using Euclid's algorithm

Highest Common Factor of 586,175,529 is 1

Step 1: Since 586 > 175, we apply the division lemma to 586 and 175, to get

586 = 175 x 3 + 61

Step 2: Since the reminder 175 ≠ 0, we apply division lemma to 61 and 175, to get

175 = 61 x 2 + 53

Step 3: We consider the new divisor 61 and the new remainder 53, and apply the division lemma to get

61 = 53 x 1 + 8

We consider the new divisor 53 and the new remainder 8,and apply the division lemma to get

53 = 8 x 6 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 586 and 175 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(53,8) = HCF(61,53) = HCF(175,61) = HCF(586,175) .

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

Step 1: Since 529 > 1, we apply the division lemma to 529 and 1, to get

529 = 1 x 529 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 529 is 1

Notice that 1 = HCF(529,1) .

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Frequently Asked Questions on HCF of 586, 175, 529 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, 175, 529?

Answer: HCF of 586, 175, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 175, 529 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 175, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.