Highest Common Factor of 9905, 6227 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 9905, 6227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9905, 6227 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 9905, 6227 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 9905, 6227 is 1.

HCF(9905, 6227) = 1

HCF of 9905, 6227 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 9905, 6227 is 1.

Highest Common Factor of 9905,6227 using Euclid's algorithm

Highest Common Factor of 9905,6227 is 1

Step 1: Since 9905 > 6227, we apply the division lemma to 9905 and 6227, to get

9905 = 6227 x 1 + 3678

Step 2: Since the reminder 6227 ≠ 0, we apply division lemma to 3678 and 6227, to get

6227 = 3678 x 1 + 2549

Step 3: We consider the new divisor 3678 and the new remainder 2549, and apply the division lemma to get

3678 = 2549 x 1 + 1129

We consider the new divisor 2549 and the new remainder 1129,and apply the division lemma to get

2549 = 1129 x 2 + 291

We consider the new divisor 1129 and the new remainder 291,and apply the division lemma to get

1129 = 291 x 3 + 256

We consider the new divisor 291 and the new remainder 256,and apply the division lemma to get

291 = 256 x 1 + 35

We consider the new divisor 256 and the new remainder 35,and apply the division lemma to get

256 = 35 x 7 + 11

We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get

35 = 11 x 3 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 9905 and 6227 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(256,35) = HCF(291,256) = HCF(1129,291) = HCF(2549,1129) = HCF(3678,2549) = HCF(6227,3678) = HCF(9905,6227) .

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Frequently Asked Questions on HCF of 9905, 6227 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 9905, 6227?

Answer: HCF of 9905, 6227 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9905, 6227 using Euclid's Algorithm?

Answer: For arbitrary numbers 9905, 6227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.