Highest Common Factor of 815, 584 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 815, 584 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 815, 584 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 815, 584 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 815, 584 is 1.

HCF(815, 584) = 1

HCF of 815, 584 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 815, 584 is 1.

Highest Common Factor of 815,584 using Euclid's algorithm

Highest Common Factor of 815,584 is 1

Step 1: Since 815 > 584, we apply the division lemma to 815 and 584, to get

815 = 584 x 1 + 231

Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 231 and 584, to get

584 = 231 x 2 + 122

Step 3: We consider the new divisor 231 and the new remainder 122, and apply the division lemma to get

231 = 122 x 1 + 109

We consider the new divisor 122 and the new remainder 109,and apply the division lemma to get

122 = 109 x 1 + 13

We consider the new divisor 109 and the new remainder 13,and apply the division lemma to get

109 = 13 x 8 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 815 and 584 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(109,13) = HCF(122,109) = HCF(231,122) = HCF(584,231) = HCF(815,584) .

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Frequently Asked Questions on HCF of 815, 584 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 815, 584?

Answer: HCF of 815, 584 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 815, 584 using Euclid's Algorithm?

Answer: For arbitrary numbers 815, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.