Highest Common Factor of 8405, 2274 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 8405, 2274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8405, 2274 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 8405, 2274 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 8405, 2274 is 1.

HCF(8405, 2274) = 1

HCF of 8405, 2274 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 8405, 2274 is 1.

Highest Common Factor of 8405,2274 using Euclid's algorithm

Highest Common Factor of 8405,2274 is 1

Step 1: Since 8405 > 2274, we apply the division lemma to 8405 and 2274, to get

8405 = 2274 x 3 + 1583

Step 2: Since the reminder 2274 ≠ 0, we apply division lemma to 1583 and 2274, to get

2274 = 1583 x 1 + 691

Step 3: We consider the new divisor 1583 and the new remainder 691, and apply the division lemma to get

1583 = 691 x 2 + 201

We consider the new divisor 691 and the new remainder 201,and apply the division lemma to get

691 = 201 x 3 + 88

We consider the new divisor 201 and the new remainder 88,and apply the division lemma to get

201 = 88 x 2 + 25

We consider the new divisor 88 and the new remainder 25,and apply the division lemma to get

88 = 25 x 3 + 13

We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get

25 = 13 x 1 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8405 and 2274 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(88,25) = HCF(201,88) = HCF(691,201) = HCF(1583,691) = HCF(2274,1583) = HCF(8405,2274) .

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Frequently Asked Questions on HCF of 8405, 2274 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 8405, 2274?

Answer: HCF of 8405, 2274 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8405, 2274 using Euclid's Algorithm?

Answer: For arbitrary numbers 8405, 2274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.