Highest Common Factor of 171, 413, 344 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 171, 413, 344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 171, 413, 344 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 171, 413, 344 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 171, 413, 344 is 1.

HCF(171, 413, 344) = 1

HCF of 171, 413, 344 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 171, 413, 344 is 1.

Highest Common Factor of 171,413,344 using Euclid's algorithm

Highest Common Factor of 171,413,344 is 1

Step 1: Since 413 > 171, we apply the division lemma to 413 and 171, to get

413 = 171 x 2 + 71

Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 71 and 171, to get

171 = 71 x 2 + 29

Step 3: 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 171 and 413 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(71,29) = HCF(171,71) = HCF(413,171) .

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

Step 1: Since 344 > 1, we apply the division lemma to 344 and 1, to get

344 = 1 x 344 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 344 is 1

Notice that 1 = HCF(344,1) .

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Frequently Asked Questions on HCF of 171, 413, 344 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 171, 413, 344?

Answer: HCF of 171, 413, 344 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 171, 413, 344 using Euclid's Algorithm?

Answer: For arbitrary numbers 171, 413, 344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.