Highest Common Factor of 514, 848, 516 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, 848, 516 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 848, 516 is 2 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, 848, 516 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, 848, 516 is 2.

HCF(514, 848, 516) = 2

HCF of 514, 848, 516 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, 848, 516 is 2.

Highest Common Factor of 514,848,516 using Euclid's algorithm

Highest Common Factor of 514,848,516 is 2

Step 1: Since 848 > 514, we apply the division lemma to 848 and 514, to get

848 = 514 x 1 + 334

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 334 and 514, to get

514 = 334 x 1 + 180

Step 3: We consider the new divisor 334 and the new remainder 180, and apply the division lemma to get

334 = 180 x 1 + 154

We consider the new divisor 180 and the new remainder 154,and apply the division lemma to get

180 = 154 x 1 + 26

We consider the new divisor 154 and the new remainder 26,and apply the division lemma to get

154 = 26 x 5 + 24

We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get

26 = 24 x 1 + 2

We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 848 is 2

Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(154,26) = HCF(180,154) = HCF(334,180) = HCF(514,334) = HCF(848,514) .

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

Step 1: Since 516 > 2, we apply the division lemma to 516 and 2, to get

516 = 2 x 258 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 516 is 2

Notice that 2 = HCF(516,2) .

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Frequently Asked Questions on HCF of 514, 848, 516 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, 848, 516?

Answer: HCF of 514, 848, 516 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 848, 516 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 848, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.