Highest Common Factor of 8051, 6296 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 8051, 6296 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8051, 6296 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 8051, 6296 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 8051, 6296 is 1.

HCF(8051, 6296) = 1

HCF of 8051, 6296 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 8051, 6296 is 1.

Highest Common Factor of 8051,6296 using Euclid's algorithm

Highest Common Factor of 8051,6296 is 1

Step 1: Since 8051 > 6296, we apply the division lemma to 8051 and 6296, to get

8051 = 6296 x 1 + 1755

Step 2: Since the reminder 6296 ≠ 0, we apply division lemma to 1755 and 6296, to get

6296 = 1755 x 3 + 1031

Step 3: We consider the new divisor 1755 and the new remainder 1031, and apply the division lemma to get

1755 = 1031 x 1 + 724

We consider the new divisor 1031 and the new remainder 724,and apply the division lemma to get

1031 = 724 x 1 + 307

We consider the new divisor 724 and the new remainder 307,and apply the division lemma to get

724 = 307 x 2 + 110

We consider the new divisor 307 and the new remainder 110,and apply the division lemma to get

307 = 110 x 2 + 87

We consider the new divisor 110 and the new remainder 87,and apply the division lemma to get

110 = 87 x 1 + 23

We consider the new divisor 87 and the new remainder 23,and apply the division lemma to get

87 = 23 x 3 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 8051 and 6296 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(87,23) = HCF(110,87) = HCF(307,110) = HCF(724,307) = HCF(1031,724) = HCF(1755,1031) = HCF(6296,1755) = HCF(8051,6296) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8051, 6296 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 8051, 6296?

Answer: HCF of 8051, 6296 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8051, 6296 using Euclid's Algorithm?

Answer: For arbitrary numbers 8051, 6296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.