Highest Common Factor of 81, 66, 406 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 81, 66, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 81, 66, 406 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 81, 66, 406 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 81, 66, 406 is 1.

HCF(81, 66, 406) = 1

HCF of 81, 66, 406 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 81, 66, 406 is 1.

Highest Common Factor of 81,66,406 using Euclid's algorithm

Highest Common Factor of 81,66,406 is 1

Step 1: Since 81 > 66, we apply the division lemma to 81 and 66, to get

81 = 66 x 1 + 15

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 15 and 66, to get

66 = 15 x 4 + 6

Step 3: We consider the new divisor 15 and the new remainder 6, and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 81 and 66 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(66,15) = HCF(81,66) .

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

Step 1: Since 406 > 3, we apply the division lemma to 406 and 3, to get

406 = 3 x 135 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 406 is 1

Notice that 1 = HCF(3,1) = HCF(406,3) .

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Frequently Asked Questions on HCF of 81, 66, 406 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 81, 66, 406?

Answer: HCF of 81, 66, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 81, 66, 406 using Euclid's Algorithm?

Answer: For arbitrary numbers 81, 66, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.