Highest Common Factor of 576, 984, 517 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 576, 984, 517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 576, 984, 517 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 576, 984, 517 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 576, 984, 517 is 1.

HCF(576, 984, 517) = 1

HCF of 576, 984, 517 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 576, 984, 517 is 1.

Highest Common Factor of 576,984,517 using Euclid's algorithm

Highest Common Factor of 576,984,517 is 1

Step 1: Since 984 > 576, we apply the division lemma to 984 and 576, to get

984 = 576 x 1 + 408

Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 408 and 576, to get

576 = 408 x 1 + 168

Step 3: We consider the new divisor 408 and the new remainder 168, and apply the division lemma to get

408 = 168 x 2 + 72

We consider the new divisor 168 and the new remainder 72,and apply the division lemma to get

168 = 72 x 2 + 24

We consider the new divisor 72 and the new remainder 24,and apply the division lemma to get

72 = 24 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 576 and 984 is 24

Notice that 24 = HCF(72,24) = HCF(168,72) = HCF(408,168) = HCF(576,408) = HCF(984,576) .

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

Step 1: Since 517 > 24, we apply the division lemma to 517 and 24, to get

517 = 24 x 21 + 13

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 13 and 24, to get

24 = 13 x 1 + 11

Step 3: We consider the new divisor 13 and the new remainder 11, and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 24 and 517 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(517,24) .

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Frequently Asked Questions on HCF of 576, 984, 517 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 576, 984, 517?

Answer: HCF of 576, 984, 517 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 576, 984, 517 using Euclid's Algorithm?

Answer: For arbitrary numbers 576, 984, 517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.