Highest Common Factor of 514, 2349, 5116 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 514, 2349, 5116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 2349, 5116 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 514, 2349, 5116 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 514, 2349, 5116 is 1.

HCF(514, 2349, 5116) = 1

HCF of 514, 2349, 5116 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 514, 2349, 5116 is 1.

Highest Common Factor of 514,2349,5116 using Euclid's algorithm

Highest Common Factor of 514,2349,5116 is 1

Step 1: Since 2349 > 514, we apply the division lemma to 2349 and 514, to get

2349 = 514 x 4 + 293

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 293 and 514, to get

514 = 293 x 1 + 221

Step 3: We consider the new divisor 293 and the new remainder 221, and apply the division lemma to get

293 = 221 x 1 + 72

We consider the new divisor 221 and the new remainder 72,and apply the division lemma to get

221 = 72 x 3 + 5

We consider the new divisor 72 and the new remainder 5,and apply the division lemma to get

72 = 5 x 14 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 514 and 2349 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(72,5) = HCF(221,72) = HCF(293,221) = HCF(514,293) = HCF(2349,514) .

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

Step 1: Since 5116 > 1, we apply the division lemma to 5116 and 1, to get

5116 = 1 x 5116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5116 is 1

Notice that 1 = HCF(5116,1) .

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Frequently Asked Questions on HCF of 514, 2349, 5116 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 514, 2349, 5116?

Answer: HCF of 514, 2349, 5116 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 2349, 5116 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 2349, 5116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.