Highest Common Factor of 2217, 8566, 81252 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 2217, 8566, 81252 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2217, 8566, 81252 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 2217, 8566, 81252 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 2217, 8566, 81252 is 1.

HCF(2217, 8566, 81252) = 1

HCF of 2217, 8566, 81252 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 2217, 8566, 81252 is 1.

Highest Common Factor of 2217,8566,81252 using Euclid's algorithm

Highest Common Factor of 2217,8566,81252 is 1

Step 1: Since 8566 > 2217, we apply the division lemma to 8566 and 2217, to get

8566 = 2217 x 3 + 1915

Step 2: Since the reminder 2217 ≠ 0, we apply division lemma to 1915 and 2217, to get

2217 = 1915 x 1 + 302

Step 3: We consider the new divisor 1915 and the new remainder 302, and apply the division lemma to get

1915 = 302 x 6 + 103

We consider the new divisor 302 and the new remainder 103,and apply the division lemma to get

302 = 103 x 2 + 96

We consider the new divisor 103 and the new remainder 96,and apply the division lemma to get

103 = 96 x 1 + 7

We consider the new divisor 96 and the new remainder 7,and apply the division lemma to get

96 = 7 x 13 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 2217 and 8566 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(96,7) = HCF(103,96) = HCF(302,103) = HCF(1915,302) = HCF(2217,1915) = HCF(8566,2217) .

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

Step 1: Since 81252 > 1, we apply the division lemma to 81252 and 1, to get

81252 = 1 x 81252 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 81252 is 1

Notice that 1 = HCF(81252,1) .

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Frequently Asked Questions on HCF of 2217, 8566, 81252 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 2217, 8566, 81252?

Answer: HCF of 2217, 8566, 81252 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2217, 8566, 81252 using Euclid's Algorithm?

Answer: For arbitrary numbers 2217, 8566, 81252 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.