Highest Common Factor of 514, 811, 972 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, 811, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 811, 972 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, 811, 972 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, 811, 972 is 1.

HCF(514, 811, 972) = 1

HCF of 514, 811, 972 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, 811, 972 is 1.

Highest Common Factor of 514,811,972 using Euclid's algorithm

Highest Common Factor of 514,811,972 is 1

Step 1: Since 811 > 514, we apply the division lemma to 811 and 514, to get

811 = 514 x 1 + 297

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 297 and 514, to get

514 = 297 x 1 + 217

Step 3: We consider the new divisor 297 and the new remainder 217, and apply the division lemma to get

297 = 217 x 1 + 80

We consider the new divisor 217 and the new remainder 80,and apply the division lemma to get

217 = 80 x 2 + 57

We consider the new divisor 80 and the new remainder 57,and apply the division lemma to get

80 = 57 x 1 + 23

We consider the new divisor 57 and the new remainder 23,and apply the division lemma to get

57 = 23 x 2 + 11

We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get

23 = 11 x 2 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 514 and 811 is 1

Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(57,23) = HCF(80,57) = HCF(217,80) = HCF(297,217) = HCF(514,297) = HCF(811,514) .

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

Step 1: Since 972 > 1, we apply the division lemma to 972 and 1, to get

972 = 1 x 972 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 972 is 1

Notice that 1 = HCF(972,1) .

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Frequently Asked Questions on HCF of 514, 811, 972 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, 811, 972?

Answer: HCF of 514, 811, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 811, 972 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 811, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.