Highest Common Factor of 514, 287, 12 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, 287, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 287, 12 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, 287, 12 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, 287, 12 is 1.

HCF(514, 287, 12) = 1

HCF of 514, 287, 12 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, 287, 12 is 1.

Highest Common Factor of 514,287,12 using Euclid's algorithm

Highest Common Factor of 514,287,12 is 1

Step 1: Since 514 > 287, we apply the division lemma to 514 and 287, to get

514 = 287 x 1 + 227

Step 2: Since the reminder 287 ≠ 0, we apply division lemma to 227 and 287, to get

287 = 227 x 1 + 60

Step 3: We consider the new divisor 227 and the new remainder 60, and apply the division lemma to get

227 = 60 x 3 + 47

We consider the new divisor 60 and the new remainder 47,and apply the division lemma to get

60 = 47 x 1 + 13

We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get

47 = 13 x 3 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 287 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(60,47) = HCF(227,60) = HCF(287,227) = HCF(514,287) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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Frequently Asked Questions on HCF of 514, 287, 12 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, 287, 12?

Answer: HCF of 514, 287, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 287, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 287, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.