Highest Common Factor of 3149, 8197, 21895 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 3149, 8197, 21895 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3149, 8197, 21895 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 3149, 8197, 21895 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 3149, 8197, 21895 is 1.

HCF(3149, 8197, 21895) = 1

HCF of 3149, 8197, 21895 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 3149, 8197, 21895 is 1.

Highest Common Factor of 3149,8197,21895 using Euclid's algorithm

Highest Common Factor of 3149,8197,21895 is 1

Step 1: Since 8197 > 3149, we apply the division lemma to 8197 and 3149, to get

8197 = 3149 x 2 + 1899

Step 2: Since the reminder 3149 ≠ 0, we apply division lemma to 1899 and 3149, to get

3149 = 1899 x 1 + 1250

Step 3: We consider the new divisor 1899 and the new remainder 1250, and apply the division lemma to get

1899 = 1250 x 1 + 649

We consider the new divisor 1250 and the new remainder 649,and apply the division lemma to get

1250 = 649 x 1 + 601

We consider the new divisor 649 and the new remainder 601,and apply the division lemma to get

649 = 601 x 1 + 48

We consider the new divisor 601 and the new remainder 48,and apply the division lemma to get

601 = 48 x 12 + 25

We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get

48 = 25 x 1 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 3149 and 8197 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(601,48) = HCF(649,601) = HCF(1250,649) = HCF(1899,1250) = HCF(3149,1899) = HCF(8197,3149) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 21895 > 1, we apply the division lemma to 21895 and 1, to get

21895 = 1 x 21895 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21895 is 1

Notice that 1 = HCF(21895,1) .

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Frequently Asked Questions on HCF of 3149, 8197, 21895 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 3149, 8197, 21895?

Answer: HCF of 3149, 8197, 21895 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3149, 8197, 21895 using Euclid's Algorithm?

Answer: For arbitrary numbers 3149, 8197, 21895 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.