Highest Common Factor of 512, 851 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 512, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 851 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 512, 851 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 512, 851 is 1.

HCF(512, 851) = 1

HCF of 512, 851 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 512, 851 is 1.

Highest Common Factor of 512,851 using Euclid's algorithm

Highest Common Factor of 512,851 is 1

Step 1: Since 851 > 512, we apply the division lemma to 851 and 512, to get

851 = 512 x 1 + 339

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 339 and 512, to get

512 = 339 x 1 + 173

Step 3: We consider the new divisor 339 and the new remainder 173, and apply the division lemma to get

339 = 173 x 1 + 166

We consider the new divisor 173 and the new remainder 166,and apply the division lemma to get

173 = 166 x 1 + 7

We consider the new divisor 166 and the new remainder 7,and apply the division lemma to get

166 = 7 x 23 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 512 and 851 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(166,7) = HCF(173,166) = HCF(339,173) = HCF(512,339) = HCF(851,512) .

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Frequently Asked Questions on HCF of 512, 851 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 512, 851?

Answer: HCF of 512, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 851 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.