Highest Common Factor of 582, 2123 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 582, 2123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 582, 2123 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 582, 2123 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 582, 2123 is 1.

HCF(582, 2123) = 1

HCF of 582, 2123 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 582, 2123 is 1.

Highest Common Factor of 582,2123 using Euclid's algorithm

Highest Common Factor of 582,2123 is 1

Step 1: Since 2123 > 582, we apply the division lemma to 2123 and 582, to get

2123 = 582 x 3 + 377

Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 377 and 582, to get

582 = 377 x 1 + 205

Step 3: We consider the new divisor 377 and the new remainder 205, and apply the division lemma to get

377 = 205 x 1 + 172

We consider the new divisor 205 and the new remainder 172,and apply the division lemma to get

205 = 172 x 1 + 33

We consider the new divisor 172 and the new remainder 33,and apply the division lemma to get

172 = 33 x 5 + 7

We consider the new divisor 33 and the new remainder 7,and apply the division lemma to get

33 = 7 x 4 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 582 and 2123 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(172,33) = HCF(205,172) = HCF(377,205) = HCF(582,377) = HCF(2123,582) .

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Frequently Asked Questions on HCF of 582, 2123 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 582, 2123?

Answer: HCF of 582, 2123 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 582, 2123 using Euclid's Algorithm?

Answer: For arbitrary numbers 582, 2123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.