Highest Common Factor of 317, 523, 473 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 317, 523, 473 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 317, 523, 473 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 317, 523, 473 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 317, 523, 473 is 1.

HCF(317, 523, 473) = 1

HCF of 317, 523, 473 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 317, 523, 473 is 1.

Highest Common Factor of 317,523,473 using Euclid's algorithm

Highest Common Factor of 317,523,473 is 1

Step 1: Since 523 > 317, we apply the division lemma to 523 and 317, to get

523 = 317 x 1 + 206

Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 206 and 317, to get

317 = 206 x 1 + 111

Step 3: We consider the new divisor 206 and the new remainder 111, and apply the division lemma to get

206 = 111 x 1 + 95

We consider the new divisor 111 and the new remainder 95,and apply the division lemma to get

111 = 95 x 1 + 16

We consider the new divisor 95 and the new remainder 16,and apply the division lemma to get

95 = 16 x 5 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 317 and 523 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(95,16) = HCF(111,95) = HCF(206,111) = HCF(317,206) = HCF(523,317) .

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

Step 1: Since 473 > 1, we apply the division lemma to 473 and 1, to get

473 = 1 x 473 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 473 is 1

Notice that 1 = HCF(473,1) .

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Frequently Asked Questions on HCF of 317, 523, 473 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 317, 523, 473?

Answer: HCF of 317, 523, 473 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 317, 523, 473 using Euclid's Algorithm?

Answer: For arbitrary numbers 317, 523, 473 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.