Highest Common Factor of 817, 313, 127 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 817, 313, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 817, 313, 127 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 817, 313, 127 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 817, 313, 127 is 1.

HCF(817, 313, 127) = 1

HCF of 817, 313, 127 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 817, 313, 127 is 1.

Highest Common Factor of 817,313,127 using Euclid's algorithm

Highest Common Factor of 817,313,127 is 1

Step 1: Since 817 > 313, we apply the division lemma to 817 and 313, to get

817 = 313 x 2 + 191

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 191 and 313, to get

313 = 191 x 1 + 122

Step 3: We consider the new divisor 191 and the new remainder 122, and apply the division lemma to get

191 = 122 x 1 + 69

We consider the new divisor 122 and the new remainder 69,and apply the division lemma to get

122 = 69 x 1 + 53

We consider the new divisor 69 and the new remainder 53,and apply the division lemma to get

69 = 53 x 1 + 16

We consider the new divisor 53 and the new remainder 16,and apply the division lemma to get

53 = 16 x 3 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 817 and 313 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(53,16) = HCF(69,53) = HCF(122,69) = HCF(191,122) = HCF(313,191) = HCF(817,313) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 127 > 1, we apply the division lemma to 127 and 1, to get

127 = 1 x 127 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 127 is 1

Notice that 1 = HCF(127,1) .

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Frequently Asked Questions on HCF of 817, 313, 127 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 817, 313, 127?

Answer: HCF of 817, 313, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 817, 313, 127 using Euclid's Algorithm?

Answer: For arbitrary numbers 817, 313, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.