Highest Common Factor of 641, 821, 131 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, 821, 131 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 641, 821, 131 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, 821, 131 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, 821, 131 is 1.

HCF(641, 821, 131) = 1

HCF of 641, 821, 131 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, 821, 131 is 1.

Highest Common Factor of 641,821,131 using Euclid's algorithm

Highest Common Factor of 641,821,131 is 1

Step 1: Since 821 > 641, we apply the division lemma to 821 and 641, to get

821 = 641 x 1 + 180

Step 2: Since the reminder 641 ≠ 0, we apply division lemma to 180 and 641, to get

641 = 180 x 3 + 101

Step 3: We consider the new divisor 180 and the new remainder 101, and apply the division lemma to get

180 = 101 x 1 + 79

We consider the new divisor 101 and the new remainder 79,and apply the division lemma to get

101 = 79 x 1 + 22

We consider the new divisor 79 and the new remainder 22,and apply the division lemma to get

79 = 22 x 3 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 641 and 821 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(79,22) = HCF(101,79) = HCF(180,101) = HCF(641,180) = HCF(821,641) .

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

Step 1: Since 131 > 1, we apply the division lemma to 131 and 1, to get

131 = 1 x 131 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 131 is 1

Notice that 1 = HCF(131,1) .

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Frequently Asked Questions on HCF of 641, 821, 131 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, 821, 131?

Answer: HCF of 641, 821, 131 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 641, 821, 131 using Euclid's Algorithm?

Answer: For arbitrary numbers 641, 821, 131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.