Highest Common Factor of 8228, 9291 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 8228, 9291 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8228, 9291 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 8228, 9291 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 8228, 9291 is 1.

HCF(8228, 9291) = 1

HCF of 8228, 9291 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 8228, 9291 is 1.

Highest Common Factor of 8228,9291 using Euclid's algorithm

Highest Common Factor of 8228,9291 is 1

Step 1: Since 9291 > 8228, we apply the division lemma to 9291 and 8228, to get

9291 = 8228 x 1 + 1063

Step 2: Since the reminder 8228 ≠ 0, we apply division lemma to 1063 and 8228, to get

8228 = 1063 x 7 + 787

Step 3: We consider the new divisor 1063 and the new remainder 787, and apply the division lemma to get

1063 = 787 x 1 + 276

We consider the new divisor 787 and the new remainder 276,and apply the division lemma to get

787 = 276 x 2 + 235

We consider the new divisor 276 and the new remainder 235,and apply the division lemma to get

276 = 235 x 1 + 41

We consider the new divisor 235 and the new remainder 41,and apply the division lemma to get

235 = 41 x 5 + 30

We consider the new divisor 41 and the new remainder 30,and apply the division lemma to get

41 = 30 x 1 + 11

We consider the new divisor 30 and the new remainder 11,and apply the division lemma to get

30 = 11 x 2 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 8228 and 9291 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(30,11) = HCF(41,30) = HCF(235,41) = HCF(276,235) = HCF(787,276) = HCF(1063,787) = HCF(8228,1063) = HCF(9291,8228) .

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Frequently Asked Questions on HCF of 8228, 9291 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 8228, 9291?

Answer: HCF of 8228, 9291 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8228, 9291 using Euclid's Algorithm?

Answer: For arbitrary numbers 8228, 9291 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.