Highest Common Factor of 585, 843, 258 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, 843, 258 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 843, 258 is 3 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, 843, 258 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, 843, 258 is 3.

HCF(585, 843, 258) = 3

HCF of 585, 843, 258 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, 843, 258 is 3.

Highest Common Factor of 585,843,258 using Euclid's algorithm

Highest Common Factor of 585,843,258 is 3

Step 1: Since 843 > 585, we apply the division lemma to 843 and 585, to get

843 = 585 x 1 + 258

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 258 and 585, to get

585 = 258 x 2 + 69

Step 3: We consider the new divisor 258 and the new remainder 69, and apply the division lemma to get

258 = 69 x 3 + 51

We consider the new divisor 69 and the new remainder 51,and apply the division lemma to get

69 = 51 x 1 + 18

We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get

51 = 18 x 2 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 585 and 843 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(69,51) = HCF(258,69) = HCF(585,258) = HCF(843,585) .

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

Step 1: Since 258 > 3, we apply the division lemma to 258 and 3, to get

258 = 3 x 86 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 258 is 3

Notice that 3 = HCF(258,3) .

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Frequently Asked Questions on HCF of 585, 843, 258 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, 843, 258?

Answer: HCF of 585, 843, 258 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 843, 258 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 843, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.