Highest Common Factor of 585, 518 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 585, 518 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 518 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 585, 518 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 585, 518 is 1.

HCF(585, 518) = 1

HCF of 585, 518 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 585, 518 is 1.

Highest Common Factor of 585,518 using Euclid's algorithm

Highest Common Factor of 585,518 is 1

Step 1: Since 585 > 518, we apply the division lemma to 585 and 518, to get

585 = 518 x 1 + 67

Step 2: Since the reminder 518 ≠ 0, we apply division lemma to 67 and 518, to get

518 = 67 x 7 + 49

Step 3: We consider the new divisor 67 and the new remainder 49, and apply the division lemma to get

67 = 49 x 1 + 18

We consider the new divisor 49 and the new remainder 18,and apply the division lemma to get

49 = 18 x 2 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 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 585 and 518 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(49,18) = HCF(67,49) = HCF(518,67) = HCF(585,518) .

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Frequently Asked Questions on HCF of 585, 518 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 585, 518?

Answer: HCF of 585, 518 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 518 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 518 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.