Highest Common Factor of 417, 582, 419 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 417, 582, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 582, 419 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 417, 582, 419 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 417, 582, 419 is 1.

HCF(417, 582, 419) = 1

HCF of 417, 582, 419 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 417, 582, 419 is 1.

Highest Common Factor of 417,582,419 using Euclid's algorithm

Highest Common Factor of 417,582,419 is 1

Step 1: Since 582 > 417, we apply the division lemma to 582 and 417, to get

582 = 417 x 1 + 165

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 165 and 417, to get

417 = 165 x 2 + 87

Step 3: We consider the new divisor 165 and the new remainder 87, and apply the division lemma to get

165 = 87 x 1 + 78

We consider the new divisor 87 and the new remainder 78,and apply the division lemma to get

87 = 78 x 1 + 9

We consider the new divisor 78 and the new remainder 9,and apply the division lemma to get

78 = 9 x 8 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 582 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(78,9) = HCF(87,78) = HCF(165,87) = HCF(417,165) = HCF(582,417) .

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

Step 1: Since 419 > 3, we apply the division lemma to 419 and 3, to get

419 = 3 x 139 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 419 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(419,3) .

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Frequently Asked Questions on HCF of 417, 582, 419 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 417, 582, 419?

Answer: HCF of 417, 582, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 582, 419 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 582, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.