Highest Common Factor of 6016, 9903 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 6016, 9903 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6016, 9903 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 6016, 9903 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 6016, 9903 is 1.

HCF(6016, 9903) = 1

HCF of 6016, 9903 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 6016, 9903 is 1.

Highest Common Factor of 6016,9903 using Euclid's algorithm

Highest Common Factor of 6016,9903 is 1

Step 1: Since 9903 > 6016, we apply the division lemma to 9903 and 6016, to get

9903 = 6016 x 1 + 3887

Step 2: Since the reminder 6016 ≠ 0, we apply division lemma to 3887 and 6016, to get

6016 = 3887 x 1 + 2129

Step 3: We consider the new divisor 3887 and the new remainder 2129, and apply the division lemma to get

3887 = 2129 x 1 + 1758

We consider the new divisor 2129 and the new remainder 1758,and apply the division lemma to get

2129 = 1758 x 1 + 371

We consider the new divisor 1758 and the new remainder 371,and apply the division lemma to get

1758 = 371 x 4 + 274

We consider the new divisor 371 and the new remainder 274,and apply the division lemma to get

371 = 274 x 1 + 97

We consider the new divisor 274 and the new remainder 97,and apply the division lemma to get

274 = 97 x 2 + 80

We consider the new divisor 97 and the new remainder 80,and apply the division lemma to get

97 = 80 x 1 + 17

We consider the new divisor 80 and the new remainder 17,and apply the division lemma to get

80 = 17 x 4 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 6016 and 9903 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(80,17) = HCF(97,80) = HCF(274,97) = HCF(371,274) = HCF(1758,371) = HCF(2129,1758) = HCF(3887,2129) = HCF(6016,3887) = HCF(9903,6016) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 6016, 9903 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 6016, 9903?

Answer: HCF of 6016, 9903 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6016, 9903 using Euclid's Algorithm?

Answer: For arbitrary numbers 6016, 9903 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.