Highest Common Factor of 8206, 463 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 8206, 463 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8206, 463 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 8206, 463 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 8206, 463 is 1.

HCF(8206, 463) = 1

HCF of 8206, 463 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 8206, 463 is 1.

Highest Common Factor of 8206,463 using Euclid's algorithm

Highest Common Factor of 8206,463 is 1

Step 1: Since 8206 > 463, we apply the division lemma to 8206 and 463, to get

8206 = 463 x 17 + 335

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 335 and 463, to get

463 = 335 x 1 + 128

Step 3: We consider the new divisor 335 and the new remainder 128, and apply the division lemma to get

335 = 128 x 2 + 79

We consider the new divisor 128 and the new remainder 79,and apply the division lemma to get

128 = 79 x 1 + 49

We consider the new divisor 79 and the new remainder 49,and apply the division lemma to get

79 = 49 x 1 + 30

We consider the new divisor 49 and the new remainder 30,and apply the division lemma to get

49 = 30 x 1 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 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 8206 and 463 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(49,30) = HCF(79,49) = HCF(128,79) = HCF(335,128) = HCF(463,335) = HCF(8206,463) .

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Frequently Asked Questions on HCF of 8206, 463 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 8206, 463?

Answer: HCF of 8206, 463 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8206, 463 using Euclid's Algorithm?

Answer: For arbitrary numbers 8206, 463 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.