Highest Common Factor of 586, 843, 878 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 586, 843, 878 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 843, 878 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 586, 843, 878 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 586, 843, 878 is 1.

HCF(586, 843, 878) = 1

HCF of 586, 843, 878 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 586, 843, 878 is 1.

Highest Common Factor of 586,843,878 using Euclid's algorithm

Highest Common Factor of 586,843,878 is 1

Step 1: Since 843 > 586, we apply the division lemma to 843 and 586, to get

843 = 586 x 1 + 257

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 257 and 586, to get

586 = 257 x 2 + 72

Step 3: We consider the new divisor 257 and the new remainder 72, and apply the division lemma to get

257 = 72 x 3 + 41

We consider the new divisor 72 and the new remainder 41,and apply the division lemma to get

72 = 41 x 1 + 31

We consider the new divisor 41 and the new remainder 31,and apply the division lemma to get

41 = 31 x 1 + 10

We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get

31 = 10 x 3 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 586 and 843 is 1

Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(41,31) = HCF(72,41) = HCF(257,72) = HCF(586,257) = HCF(843,586) .

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

Step 1: Since 878 > 1, we apply the division lemma to 878 and 1, to get

878 = 1 x 878 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 878 is 1

Notice that 1 = HCF(878,1) .

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Frequently Asked Questions on HCF of 586, 843, 878 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 586, 843, 878?

Answer: HCF of 586, 843, 878 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 843, 878 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 843, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.