Highest Common Factor of 317, 591, 168 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, 591, 168 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 317, 591, 168 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, 591, 168 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, 591, 168 is 1.

HCF(317, 591, 168) = 1

HCF of 317, 591, 168 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, 591, 168 is 1.

Highest Common Factor of 317,591,168 using Euclid's algorithm

Highest Common Factor of 317,591,168 is 1

Step 1: Since 591 > 317, we apply the division lemma to 591 and 317, to get

591 = 317 x 1 + 274

Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 274 and 317, to get

317 = 274 x 1 + 43

Step 3: We consider the new divisor 274 and the new remainder 43, and apply the division lemma to get

274 = 43 x 6 + 16

We consider the new divisor 43 and the new remainder 16,and apply the division lemma to get

43 = 16 x 2 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 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 317 and 591 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(43,16) = HCF(274,43) = HCF(317,274) = HCF(591,317) .

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

Step 1: Since 168 > 1, we apply the division lemma to 168 and 1, to get

168 = 1 x 168 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 168 is 1

Notice that 1 = HCF(168,1) .

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Frequently Asked Questions on HCF of 317, 591, 168 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, 591, 168?

Answer: HCF of 317, 591, 168 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 317, 591, 168 using Euclid's Algorithm?

Answer: For arbitrary numbers 317, 591, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.