Highest Common Factor of 826, 2267 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 826, 2267 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 826, 2267 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 826, 2267 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 826, 2267 is 1.

HCF(826, 2267) = 1

HCF of 826, 2267 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 826, 2267 is 1.

Highest Common Factor of 826,2267 using Euclid's algorithm

Highest Common Factor of 826,2267 is 1

Step 1: Since 2267 > 826, we apply the division lemma to 2267 and 826, to get

2267 = 826 x 2 + 615

Step 2: Since the reminder 826 ≠ 0, we apply division lemma to 615 and 826, to get

826 = 615 x 1 + 211

Step 3: We consider the new divisor 615 and the new remainder 211, and apply the division lemma to get

615 = 211 x 2 + 193

We consider the new divisor 211 and the new remainder 193,and apply the division lemma to get

211 = 193 x 1 + 18

We consider the new divisor 193 and the new remainder 18,and apply the division lemma to get

193 = 18 x 10 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 826 and 2267 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(193,18) = HCF(211,193) = HCF(615,211) = HCF(826,615) = HCF(2267,826) .

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Frequently Asked Questions on HCF of 826, 2267 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 826, 2267?

Answer: HCF of 826, 2267 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 826, 2267 using Euclid's Algorithm?

Answer: For arbitrary numbers 826, 2267 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.