Highest Common Factor of 382, 241, 659 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 382, 241, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 382, 241, 659 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 382, 241, 659 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 382, 241, 659 is 1.

HCF(382, 241, 659) = 1

HCF of 382, 241, 659 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 382, 241, 659 is 1.

Highest Common Factor of 382,241,659 using Euclid's algorithm

Highest Common Factor of 382,241,659 is 1

Step 1: Since 382 > 241, we apply the division lemma to 382 and 241, to get

382 = 241 x 1 + 141

Step 2: Since the reminder 241 ≠ 0, we apply division lemma to 141 and 241, to get

241 = 141 x 1 + 100

Step 3: We consider the new divisor 141 and the new remainder 100, and apply the division lemma to get

141 = 100 x 1 + 41

We consider the new divisor 100 and the new remainder 41,and apply the division lemma to get

100 = 41 x 2 + 18

We consider the new divisor 41 and the new remainder 18,and apply the division lemma to get

41 = 18 x 2 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 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 382 and 241 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(41,18) = HCF(100,41) = HCF(141,100) = HCF(241,141) = HCF(382,241) .

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

Step 1: Since 659 > 1, we apply the division lemma to 659 and 1, to get

659 = 1 x 659 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 659 is 1

Notice that 1 = HCF(659,1) .

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Frequently Asked Questions on HCF of 382, 241, 659 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 382, 241, 659?

Answer: HCF of 382, 241, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 382, 241, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 382, 241, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.