Highest Common Factor of 905, 3072 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 905, 3072 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 905, 3072 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 905, 3072 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 905, 3072 is 1.

HCF(905, 3072) = 1

HCF of 905, 3072 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 905, 3072 is 1.

Highest Common Factor of 905,3072 using Euclid's algorithm

Highest Common Factor of 905,3072 is 1

Step 1: Since 3072 > 905, we apply the division lemma to 3072 and 905, to get

3072 = 905 x 3 + 357

Step 2: Since the reminder 905 ≠ 0, we apply division lemma to 357 and 905, to get

905 = 357 x 2 + 191

Step 3: We consider the new divisor 357 and the new remainder 191, and apply the division lemma to get

357 = 191 x 1 + 166

We consider the new divisor 191 and the new remainder 166,and apply the division lemma to get

191 = 166 x 1 + 25

We consider the new divisor 166 and the new remainder 25,and apply the division lemma to get

166 = 25 x 6 + 16

We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get

25 = 16 x 1 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 905 and 3072 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(166,25) = HCF(191,166) = HCF(357,191) = HCF(905,357) = HCF(3072,905) .

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Frequently Asked Questions on HCF of 905, 3072 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 905, 3072?

Answer: HCF of 905, 3072 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 905, 3072 using Euclid's Algorithm?

Answer: For arbitrary numbers 905, 3072 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.