Highest Common Factor of 387, 663, 80 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 387, 663, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 387, 663, 80 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 387, 663, 80 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 387, 663, 80 is 1.

HCF(387, 663, 80) = 1

HCF of 387, 663, 80 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 387, 663, 80 is 1.

Highest Common Factor of 387,663,80 using Euclid's algorithm

Highest Common Factor of 387,663,80 is 1

Step 1: Since 663 > 387, we apply the division lemma to 663 and 387, to get

663 = 387 x 1 + 276

Step 2: Since the reminder 387 ≠ 0, we apply division lemma to 276 and 387, to get

387 = 276 x 1 + 111

Step 3: We consider the new divisor 276 and the new remainder 111, and apply the division lemma to get

276 = 111 x 2 + 54

We consider the new divisor 111 and the new remainder 54,and apply the division lemma to get

111 = 54 x 2 + 3

We consider the new divisor 54 and the new remainder 3,and apply the division lemma to get

54 = 3 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 387 and 663 is 3

Notice that 3 = HCF(54,3) = HCF(111,54) = HCF(276,111) = HCF(387,276) = HCF(663,387) .

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

Step 1: Since 80 > 3, we apply the division lemma to 80 and 3, to get

80 = 3 x 26 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 80 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(80,3) .

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Frequently Asked Questions on HCF of 387, 663, 80 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 387, 663, 80?

Answer: HCF of 387, 663, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 387, 663, 80 using Euclid's Algorithm?

Answer: For arbitrary numbers 387, 663, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.