Highest Common Factor of 517, 870, 684 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, 870, 684 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 870, 684 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, 870, 684 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, 870, 684 is 1.

HCF(517, 870, 684) = 1

HCF of 517, 870, 684 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, 870, 684 is 1.

Highest Common Factor of 517,870,684 using Euclid's algorithm

Highest Common Factor of 517,870,684 is 1

Step 1: Since 870 > 517, we apply the division lemma to 870 and 517, to get

870 = 517 x 1 + 353

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 353 and 517, to get

517 = 353 x 1 + 164

Step 3: We consider the new divisor 353 and the new remainder 164, and apply the division lemma to get

353 = 164 x 2 + 25

We consider the new divisor 164 and the new remainder 25,and apply the division lemma to get

164 = 25 x 6 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 517 and 870 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(164,25) = HCF(353,164) = HCF(517,353) = HCF(870,517) .

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

Step 1: Since 684 > 1, we apply the division lemma to 684 and 1, to get

684 = 1 x 684 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 684 is 1

Notice that 1 = HCF(684,1) .

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Frequently Asked Questions on HCF of 517, 870, 684 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, 870, 684?

Answer: HCF of 517, 870, 684 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 870, 684 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 870, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.