Highest Common Factor of 999, 582, 613 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 999, 582, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 999, 582, 613 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 999, 582, 613 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 999, 582, 613 is 1.

HCF(999, 582, 613) = 1

HCF of 999, 582, 613 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 999, 582, 613 is 1.

Highest Common Factor of 999,582,613 using Euclid's algorithm

Highest Common Factor of 999,582,613 is 1

Step 1: Since 999 > 582, we apply the division lemma to 999 and 582, to get

999 = 582 x 1 + 417

Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 417 and 582, to get

582 = 417 x 1 + 165

Step 3: We consider the new divisor 417 and the new remainder 165, and apply the division lemma to get

417 = 165 x 2 + 87

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 999 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) = HCF(999,582) .

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

Step 1: Since 613 > 3, we apply the division lemma to 613 and 3, to get

613 = 3 x 204 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 613 is 1

Notice that 1 = HCF(3,1) = HCF(613,3) .

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Frequently Asked Questions on HCF of 999, 582, 613 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 999, 582, 613?

Answer: HCF of 999, 582, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 999, 582, 613 using Euclid's Algorithm?

Answer: For arbitrary numbers 999, 582, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.