Highest Common Factor of 8997, 7151, 27113 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 8997, 7151, 27113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8997, 7151, 27113 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 8997, 7151, 27113 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 8997, 7151, 27113 is 1.

HCF(8997, 7151, 27113) = 1

HCF of 8997, 7151, 27113 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 8997, 7151, 27113 is 1.

Highest Common Factor of 8997,7151,27113 using Euclid's algorithm

Highest Common Factor of 8997,7151,27113 is 1

Step 1: Since 8997 > 7151, we apply the division lemma to 8997 and 7151, to get

8997 = 7151 x 1 + 1846

Step 2: Since the reminder 7151 ≠ 0, we apply division lemma to 1846 and 7151, to get

7151 = 1846 x 3 + 1613

Step 3: We consider the new divisor 1846 and the new remainder 1613, and apply the division lemma to get

1846 = 1613 x 1 + 233

We consider the new divisor 1613 and the new remainder 233,and apply the division lemma to get

1613 = 233 x 6 + 215

We consider the new divisor 233 and the new remainder 215,and apply the division lemma to get

233 = 215 x 1 + 18

We consider the new divisor 215 and the new remainder 18,and apply the division lemma to get

215 = 18 x 11 + 17

We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get

18 = 17 x 1 + 1

We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get

17 = 1 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8997 and 7151 is 1

Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(215,18) = HCF(233,215) = HCF(1613,233) = HCF(1846,1613) = HCF(7151,1846) = HCF(8997,7151) .

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

Step 1: Since 27113 > 1, we apply the division lemma to 27113 and 1, to get

27113 = 1 x 27113 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27113 is 1

Notice that 1 = HCF(27113,1) .

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Frequently Asked Questions on HCF of 8997, 7151, 27113 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 8997, 7151, 27113?

Answer: HCF of 8997, 7151, 27113 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8997, 7151, 27113 using Euclid's Algorithm?

Answer: For arbitrary numbers 8997, 7151, 27113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.