Highest Common Factor of 6771, 216 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 6771, 216 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 6771, 216 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 6771, 216 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 6771, 216 is 3.

HCF(6771, 216) = 3

HCF of 6771, 216 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 6771, 216 is 3.

Highest Common Factor of 6771,216 using Euclid's algorithm

Highest Common Factor of 6771,216 is 3

Step 1: Since 6771 > 216, we apply the division lemma to 6771 and 216, to get

6771 = 216 x 31 + 75

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 75 and 216, to get

216 = 75 x 2 + 66

Step 3: We consider the new divisor 75 and the new remainder 66, and apply the division lemma to get

75 = 66 x 1 + 9

We consider the new divisor 66 and the new remainder 9,and apply the division lemma to get

66 = 9 x 7 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6771 and 216 is 3

Notice that 3 = HCF(9,3) = HCF(66,9) = HCF(75,66) = HCF(216,75) = HCF(6771,216) .

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Frequently Asked Questions on HCF of 6771, 216 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 6771, 216?

Answer: HCF of 6771, 216 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6771, 216 using Euclid's Algorithm?

Answer: For arbitrary numbers 6771, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.