Highest Common Factor of 474, 683, 517 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 474, 683, 517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 474, 683, 517 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 474, 683, 517 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 474, 683, 517 is 1.

HCF(474, 683, 517) = 1

HCF of 474, 683, 517 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 474, 683, 517 is 1.

Highest Common Factor of 474,683,517 using Euclid's algorithm

Highest Common Factor of 474,683,517 is 1

Step 1: Since 683 > 474, we apply the division lemma to 683 and 474, to get

683 = 474 x 1 + 209

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 209 and 474, to get

474 = 209 x 2 + 56

Step 3: We consider the new divisor 209 and the new remainder 56, and apply the division lemma to get

209 = 56 x 3 + 41

We consider the new divisor 56 and the new remainder 41,and apply the division lemma to get

56 = 41 x 1 + 15

We consider the new divisor 41 and the new remainder 15,and apply the division lemma to get

41 = 15 x 2 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 474 and 683 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(41,15) = HCF(56,41) = HCF(209,56) = HCF(474,209) = HCF(683,474) .

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

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

517 = 1 x 517 + 0

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

Notice that 1 = HCF(517,1) .

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Frequently Asked Questions on HCF of 474, 683, 517 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 474, 683, 517?

Answer: HCF of 474, 683, 517 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 474, 683, 517 using Euclid's Algorithm?

Answer: For arbitrary numbers 474, 683, 517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.