Highest Common Factor of 512, 311 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, 311 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 311 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, 311 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, 311 is 1.

HCF(512, 311) = 1

HCF of 512, 311 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, 311 is 1.

Highest Common Factor of 512,311 using Euclid's algorithm

Highest Common Factor of 512,311 is 1

Step 1: Since 512 > 311, we apply the division lemma to 512 and 311, to get

512 = 311 x 1 + 201

Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 201 and 311, to get

311 = 201 x 1 + 110

Step 3: We consider the new divisor 201 and the new remainder 110, and apply the division lemma to get

201 = 110 x 1 + 91

We consider the new divisor 110 and the new remainder 91,and apply the division lemma to get

110 = 91 x 1 + 19

We consider the new divisor 91 and the new remainder 19,and apply the division lemma to get

91 = 19 x 4 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 512 and 311 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(91,19) = HCF(110,91) = HCF(201,110) = HCF(311,201) = HCF(512,311) .

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Frequently Asked Questions on HCF of 512, 311 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, 311?

Answer: HCF of 512, 311 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 311 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 311 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.