Highest Common Factor of 8159, 9197, 21484 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 8159, 9197, 21484 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8159, 9197, 21484 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 8159, 9197, 21484 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 8159, 9197, 21484 is 1.

HCF(8159, 9197, 21484) = 1

HCF of 8159, 9197, 21484 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 8159, 9197, 21484 is 1.

Highest Common Factor of 8159,9197,21484 using Euclid's algorithm

Highest Common Factor of 8159,9197,21484 is 1

Step 1: Since 9197 > 8159, we apply the division lemma to 9197 and 8159, to get

9197 = 8159 x 1 + 1038

Step 2: Since the reminder 8159 ≠ 0, we apply division lemma to 1038 and 8159, to get

8159 = 1038 x 7 + 893

Step 3: We consider the new divisor 1038 and the new remainder 893, and apply the division lemma to get

1038 = 893 x 1 + 145

We consider the new divisor 893 and the new remainder 145,and apply the division lemma to get

893 = 145 x 6 + 23

We consider the new divisor 145 and the new remainder 23,and apply the division lemma to get

145 = 23 x 6 + 7

We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get

23 = 7 x 3 + 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 8159 and 9197 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(145,23) = HCF(893,145) = HCF(1038,893) = HCF(8159,1038) = HCF(9197,8159) .

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

Step 1: Since 21484 > 1, we apply the division lemma to 21484 and 1, to get

21484 = 1 x 21484 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21484 is 1

Notice that 1 = HCF(21484,1) .

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Frequently Asked Questions on HCF of 8159, 9197, 21484 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 8159, 9197, 21484?

Answer: HCF of 8159, 9197, 21484 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8159, 9197, 21484 using Euclid's Algorithm?

Answer: For arbitrary numbers 8159, 9197, 21484 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.