Highest Common Factor of 663, 2186, 6065 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 663, 2186, 6065 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 2186, 6065 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 663, 2186, 6065 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 663, 2186, 6065 is 1.

HCF(663, 2186, 6065) = 1

HCF of 663, 2186, 6065 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 663, 2186, 6065 is 1.

Highest Common Factor of 663,2186,6065 using Euclid's algorithm

Highest Common Factor of 663,2186,6065 is 1

Step 1: Since 2186 > 663, we apply the division lemma to 2186 and 663, to get

2186 = 663 x 3 + 197

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 197 and 663, to get

663 = 197 x 3 + 72

Step 3: We consider the new divisor 197 and the new remainder 72, and apply the division lemma to get

197 = 72 x 2 + 53

We consider the new divisor 72 and the new remainder 53,and apply the division lemma to get

72 = 53 x 1 + 19

We consider the new divisor 53 and the new remainder 19,and apply the division lemma to get

53 = 19 x 2 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 663 and 2186 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(53,19) = HCF(72,53) = HCF(197,72) = HCF(663,197) = HCF(2186,663) .

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

Step 1: Since 6065 > 1, we apply the division lemma to 6065 and 1, to get

6065 = 1 x 6065 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6065 is 1

Notice that 1 = HCF(6065,1) .

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Frequently Asked Questions on HCF of 663, 2186, 6065 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 663, 2186, 6065?

Answer: HCF of 663, 2186, 6065 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 2186, 6065 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 2186, 6065 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.