Highest Common Factor of 517, 317, 342 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 517, 317, 342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 317, 342 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 517, 317, 342 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 517, 317, 342 is 1.

HCF(517, 317, 342) = 1

HCF of 517, 317, 342 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 517, 317, 342 is 1.

Highest Common Factor of 517,317,342 using Euclid's algorithm

Highest Common Factor of 517,317,342 is 1

Step 1: Since 517 > 317, we apply the division lemma to 517 and 317, to get

517 = 317 x 1 + 200

Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 200 and 317, to get

317 = 200 x 1 + 117

Step 3: We consider the new divisor 200 and the new remainder 117, and apply the division lemma to get

200 = 117 x 1 + 83

We consider the new divisor 117 and the new remainder 83,and apply the division lemma to get

117 = 83 x 1 + 34

We consider the new divisor 83 and the new remainder 34,and apply the division lemma to get

83 = 34 x 2 + 15

We consider the new divisor 34 and the new remainder 15,and apply the division lemma to get

34 = 15 x 2 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 517 and 317 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(34,15) = HCF(83,34) = HCF(117,83) = HCF(200,117) = HCF(317,200) = HCF(517,317) .

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

Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get

342 = 1 x 342 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1

Notice that 1 = HCF(342,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 517, 317, 342 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 517, 317, 342?

Answer: HCF of 517, 317, 342 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 317, 342 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 317, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.