Highest Common Factor of 371, 471, 663 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 371, 471, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 371, 471, 663 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 371, 471, 663 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 371, 471, 663 is 1.

HCF(371, 471, 663) = 1

HCF of 371, 471, 663 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 371, 471, 663 is 1.

Highest Common Factor of 371,471,663 using Euclid's algorithm

Highest Common Factor of 371,471,663 is 1

Step 1: Since 471 > 371, we apply the division lemma to 471 and 371, to get

471 = 371 x 1 + 100

Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 100 and 371, to get

371 = 100 x 3 + 71

Step 3: We consider the new divisor 100 and the new remainder 71, and apply the division lemma to get

100 = 71 x 1 + 29

We consider the new divisor 71 and the new remainder 29,and apply the division lemma to get

71 = 29 x 2 + 13

We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get

29 = 13 x 2 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 371 and 471 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(71,29) = HCF(100,71) = HCF(371,100) = HCF(471,371) .

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

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

663 = 1 x 663 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 663 is 1

Notice that 1 = HCF(663,1) .

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Frequently Asked Questions on HCF of 371, 471, 663 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 371, 471, 663?

Answer: HCF of 371, 471, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 371, 471, 663 using Euclid's Algorithm?

Answer: For arbitrary numbers 371, 471, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.