Highest Common Factor of 867, 566 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 867, 566 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 566 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 867, 566 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 867, 566 is 1.

HCF(867, 566) = 1

HCF of 867, 566 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 867, 566 is 1.

Highest Common Factor of 867,566 using Euclid's algorithm

Highest Common Factor of 867,566 is 1

Step 1: Since 867 > 566, we apply the division lemma to 867 and 566, to get

867 = 566 x 1 + 301

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 301 and 566, to get

566 = 301 x 1 + 265

Step 3: We consider the new divisor 301 and the new remainder 265, and apply the division lemma to get

301 = 265 x 1 + 36

We consider the new divisor 265 and the new remainder 36,and apply the division lemma to get

265 = 36 x 7 + 13

We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get

36 = 13 x 2 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 867 and 566 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(265,36) = HCF(301,265) = HCF(566,301) = HCF(867,566) .

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Frequently Asked Questions on HCF of 867, 566 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 867, 566?

Answer: HCF of 867, 566 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 566 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 566 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.