Highest Common Factor of 582, 963, 171 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 582, 963, 171 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 582, 963, 171 is 3 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 582, 963, 171 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 582, 963, 171 is 3.

HCF(582, 963, 171) = 3

HCF of 582, 963, 171 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 582, 963, 171 is 3.

Highest Common Factor of 582,963,171 using Euclid's algorithm

Highest Common Factor of 582,963,171 is 3

Step 1: Since 963 > 582, we apply the division lemma to 963 and 582, to get

963 = 582 x 1 + 381

Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 381 and 582, to get

582 = 381 x 1 + 201

Step 3: We consider the new divisor 381 and the new remainder 201, and apply the division lemma to get

381 = 201 x 1 + 180

We consider the new divisor 201 and the new remainder 180,and apply the division lemma to get

201 = 180 x 1 + 21

We consider the new divisor 180 and the new remainder 21,and apply the division lemma to get

180 = 21 x 8 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 582 and 963 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(180,21) = HCF(201,180) = HCF(381,201) = HCF(582,381) = HCF(963,582) .

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

Step 1: Since 171 > 3, we apply the division lemma to 171 and 3, to get

171 = 3 x 57 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 171 is 3

Notice that 3 = HCF(171,3) .

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Frequently Asked Questions on HCF of 582, 963, 171 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 582, 963, 171?

Answer: HCF of 582, 963, 171 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 582, 963, 171 using Euclid's Algorithm?

Answer: For arbitrary numbers 582, 963, 171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.