Highest Common Factor of 344, 529, 164 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 344, 529, 164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 344, 529, 164 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 344, 529, 164 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 344, 529, 164 is 1.

HCF(344, 529, 164) = 1

HCF of 344, 529, 164 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 344, 529, 164 is 1.

Highest Common Factor of 344,529,164 using Euclid's algorithm

Highest Common Factor of 344,529,164 is 1

Step 1: Since 529 > 344, we apply the division lemma to 529 and 344, to get

529 = 344 x 1 + 185

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 185 and 344, to get

344 = 185 x 1 + 159

Step 3: We consider the new divisor 185 and the new remainder 159, and apply the division lemma to get

185 = 159 x 1 + 26

We consider the new divisor 159 and the new remainder 26,and apply the division lemma to get

159 = 26 x 6 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 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 344 and 529 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(159,26) = HCF(185,159) = HCF(344,185) = HCF(529,344) .

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

Step 1: Since 164 > 1, we apply the division lemma to 164 and 1, to get

164 = 1 x 164 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 164 is 1

Notice that 1 = HCF(164,1) .

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Frequently Asked Questions on HCF of 344, 529, 164 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 344, 529, 164?

Answer: HCF of 344, 529, 164 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 344, 529, 164 using Euclid's Algorithm?

Answer: For arbitrary numbers 344, 529, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.