Highest Common Factor of 517, 99126 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 517, 99126 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 99126 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 517, 99126 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 517, 99126 is 1.

HCF(517, 99126) = 1

HCF of 517, 99126 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 517, 99126 is 1.

Highest Common Factor of 517,99126 using Euclid's algorithm

Highest Common Factor of 517,99126 is 1

Step 1: Since 99126 > 517, we apply the division lemma to 99126 and 517, to get

99126 = 517 x 191 + 379

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 379 and 517, to get

517 = 379 x 1 + 138

Step 3: We consider the new divisor 379 and the new remainder 138, and apply the division lemma to get

379 = 138 x 2 + 103

We consider the new divisor 138 and the new remainder 103,and apply the division lemma to get

138 = 103 x 1 + 35

We consider the new divisor 103 and the new remainder 35,and apply the division lemma to get

103 = 35 x 2 + 33

We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get

35 = 33 x 1 + 2

We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get

33 = 2 x 16 + 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 517 and 99126 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(103,35) = HCF(138,103) = HCF(379,138) = HCF(517,379) = HCF(99126,517) .

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Frequently Asked Questions on HCF of 517, 99126 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 517, 99126?

Answer: HCF of 517, 99126 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 99126 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 99126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.