Highest Common Factor of 866, 8101 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, 8101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 866, 8101 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, 8101 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, 8101 is 1.

HCF(866, 8101) = 1

HCF of 866, 8101 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, 8101 is 1.

Highest Common Factor of 866,8101 using Euclid's algorithm

Highest Common Factor of 866,8101 is 1

Step 1: Since 8101 > 866, we apply the division lemma to 8101 and 866, to get

8101 = 866 x 9 + 307

Step 2: Since the reminder 866 ≠ 0, we apply division lemma to 307 and 866, to get

866 = 307 x 2 + 252

Step 3: We consider the new divisor 307 and the new remainder 252, and apply the division lemma to get

307 = 252 x 1 + 55

We consider the new divisor 252 and the new remainder 55,and apply the division lemma to get

252 = 55 x 4 + 32

We consider the new divisor 55 and the new remainder 32,and apply the division lemma to get

55 = 32 x 1 + 23

We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get

32 = 23 x 1 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 866 and 8101 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(55,32) = HCF(252,55) = HCF(307,252) = HCF(866,307) = HCF(8101,866) .

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Frequently Asked Questions on HCF of 866, 8101 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, 8101?

Answer: HCF of 866, 8101 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 866, 8101 using Euclid's Algorithm?

Answer: For arbitrary numbers 866, 8101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.