Highest Common Factor of 851, 517 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 851, 517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 851, 517 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 851, 517 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 851, 517 is 1.

HCF(851, 517) = 1

HCF of 851, 517 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 851, 517 is 1.

Highest Common Factor of 851,517 using Euclid's algorithm

Highest Common Factor of 851,517 is 1

Step 1: Since 851 > 517, we apply the division lemma to 851 and 517, to get

851 = 517 x 1 + 334

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 334 and 517, to get

517 = 334 x 1 + 183

Step 3: We consider the new divisor 334 and the new remainder 183, and apply the division lemma to get

334 = 183 x 1 + 151

We consider the new divisor 183 and the new remainder 151,and apply the division lemma to get

183 = 151 x 1 + 32

We consider the new divisor 151 and the new remainder 32,and apply the division lemma to get

151 = 32 x 4 + 23

We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get

32 = 23 x 1 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 851 and 517 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(151,32) = HCF(183,151) = HCF(334,183) = HCF(517,334) = HCF(851,517) .

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Frequently Asked Questions on HCF of 851, 517 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 851, 517?

Answer: HCF of 851, 517 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 851, 517 using Euclid's Algorithm?

Answer: For arbitrary numbers 851, 517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.