Highest Common Factor of 8317, 1296 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 8317, 1296 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8317, 1296 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 8317, 1296 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 8317, 1296 is 1.

HCF(8317, 1296) = 1

HCF of 8317, 1296 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 8317, 1296 is 1.

Highest Common Factor of 8317,1296 using Euclid's algorithm

Highest Common Factor of 8317,1296 is 1

Step 1: Since 8317 > 1296, we apply the division lemma to 8317 and 1296, to get

8317 = 1296 x 6 + 541

Step 2: Since the reminder 1296 ≠ 0, we apply division lemma to 541 and 1296, to get

1296 = 541 x 2 + 214

Step 3: We consider the new divisor 541 and the new remainder 214, and apply the division lemma to get

541 = 214 x 2 + 113

We consider the new divisor 214 and the new remainder 113,and apply the division lemma to get

214 = 113 x 1 + 101

We consider the new divisor 113 and the new remainder 101,and apply the division lemma to get

113 = 101 x 1 + 12

We consider the new divisor 101 and the new remainder 12,and apply the division lemma to get

101 = 12 x 8 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 8317 and 1296 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(101,12) = HCF(113,101) = HCF(214,113) = HCF(541,214) = HCF(1296,541) = HCF(8317,1296) .

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Frequently Asked Questions on HCF of 8317, 1296 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 8317, 1296?

Answer: HCF of 8317, 1296 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8317, 1296 using Euclid's Algorithm?

Answer: For arbitrary numbers 8317, 1296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.