Highest Common Factor of 641, 114, 471 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 641, 114, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 641, 114, 471 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 641, 114, 471 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 641, 114, 471 is 1.

HCF(641, 114, 471) = 1

HCF of 641, 114, 471 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 641, 114, 471 is 1.

Highest Common Factor of 641,114,471 using Euclid's algorithm

Highest Common Factor of 641,114,471 is 1

Step 1: Since 641 > 114, we apply the division lemma to 641 and 114, to get

641 = 114 x 5 + 71

Step 2: Since the reminder 114 ≠ 0, we apply division lemma to 71 and 114, to get

114 = 71 x 1 + 43

Step 3: We consider the new divisor 71 and the new remainder 43, and apply the division lemma to get

71 = 43 x 1 + 28

We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get

43 = 28 x 1 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

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 641 and 114 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(71,43) = HCF(114,71) = HCF(641,114) .

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

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

471 = 1 x 471 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 471 is 1

Notice that 1 = HCF(471,1) .

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Frequently Asked Questions on HCF of 641, 114, 471 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 641, 114, 471?

Answer: HCF of 641, 114, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 641, 114, 471 using Euclid's Algorithm?

Answer: For arbitrary numbers 641, 114, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.