Highest Common Factor of 341, 129, 115 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 341, 129, 115 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 341, 129, 115 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 341, 129, 115 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 341, 129, 115 is 1.

HCF(341, 129, 115) = 1

HCF of 341, 129, 115 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 341, 129, 115 is 1.

Highest Common Factor of 341,129,115 using Euclid's algorithm

Highest Common Factor of 341,129,115 is 1

Step 1: Since 341 > 129, we apply the division lemma to 341 and 129, to get

341 = 129 x 2 + 83

Step 2: Since the reminder 129 ≠ 0, we apply division lemma to 83 and 129, to get

129 = 83 x 1 + 46

Step 3: We consider the new divisor 83 and the new remainder 46, and apply the division lemma to get

83 = 46 x 1 + 37

We consider the new divisor 46 and the new remainder 37,and apply the division lemma to get

46 = 37 x 1 + 9

We consider the new divisor 37 and the new remainder 9,and apply the division lemma to get

37 = 9 x 4 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 341 and 129 is 1

Notice that 1 = HCF(9,1) = HCF(37,9) = HCF(46,37) = HCF(83,46) = HCF(129,83) = HCF(341,129) .

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

Step 1: Since 115 > 1, we apply the division lemma to 115 and 1, to get

115 = 1 x 115 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 115 is 1

Notice that 1 = HCF(115,1) .

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Frequently Asked Questions on HCF of 341, 129, 115 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 341, 129, 115?

Answer: HCF of 341, 129, 115 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 341, 129, 115 using Euclid's Algorithm?

Answer: For arbitrary numbers 341, 129, 115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.