Highest Common Factor of 514, 917, 27 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, 917, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 917, 27 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, 917, 27 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, 917, 27 is 1.

HCF(514, 917, 27) = 1

HCF of 514, 917, 27 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, 917, 27 is 1.

Highest Common Factor of 514,917,27 using Euclid's algorithm

Highest Common Factor of 514,917,27 is 1

Step 1: Since 917 > 514, we apply the division lemma to 917 and 514, to get

917 = 514 x 1 + 403

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 403 and 514, to get

514 = 403 x 1 + 111

Step 3: We consider the new divisor 403 and the new remainder 111, and apply the division lemma to get

403 = 111 x 3 + 70

We consider the new divisor 111 and the new remainder 70,and apply the division lemma to get

111 = 70 x 1 + 41

We consider the new divisor 70 and the new remainder 41,and apply the division lemma to get

70 = 41 x 1 + 29

We consider the new divisor 41 and the new remainder 29,and apply the division lemma to get

41 = 29 x 1 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 917 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(41,29) = HCF(70,41) = HCF(111,70) = HCF(403,111) = HCF(514,403) = HCF(917,514) .

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

Step 1: Since 27 > 1, we apply the division lemma to 27 and 1, to get

27 = 1 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27 is 1

Notice that 1 = HCF(27,1) .

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Frequently Asked Questions on HCF of 514, 917, 27 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, 917, 27?

Answer: HCF of 514, 917, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 917, 27 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 917, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.