Highest Common Factor of 866, 1586, 3815 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 866, 1586, 3815 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 866, 1586, 3815 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 866, 1586, 3815 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 866, 1586, 3815 is 1.

HCF(866, 1586, 3815) = 1

HCF of 866, 1586, 3815 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 866, 1586, 3815 is 1.

Highest Common Factor of 866,1586,3815 using Euclid's algorithm

Highest Common Factor of 866,1586,3815 is 1

Step 1: Since 1586 > 866, we apply the division lemma to 1586 and 866, to get

1586 = 866 x 1 + 720

Step 2: Since the reminder 866 ≠ 0, we apply division lemma to 720 and 866, to get

866 = 720 x 1 + 146

Step 3: We consider the new divisor 720 and the new remainder 146, and apply the division lemma to get

720 = 146 x 4 + 136

We consider the new divisor 146 and the new remainder 136,and apply the division lemma to get

146 = 136 x 1 + 10

We consider the new divisor 136 and the new remainder 10,and apply the division lemma to get

136 = 10 x 13 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 866 and 1586 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(136,10) = HCF(146,136) = HCF(720,146) = HCF(866,720) = HCF(1586,866) .

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

Step 1: Since 3815 > 2, we apply the division lemma to 3815 and 2, to get

3815 = 2 x 1907 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 3815 is 1

Notice that 1 = HCF(2,1) = HCF(3815,2) .

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Frequently Asked Questions on HCF of 866, 1586, 3815 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 866, 1586, 3815?

Answer: HCF of 866, 1586, 3815 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 866, 1586, 3815 using Euclid's Algorithm?

Answer: For arbitrary numbers 866, 1586, 3815 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.