Highest Common Factor of 521, 343 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 521, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 521, 343 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 521, 343 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 521, 343 is 1.

HCF(521, 343) = 1

HCF of 521, 343 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 521, 343 is 1.

Highest Common Factor of 521,343 using Euclid's algorithm

Highest Common Factor of 521,343 is 1

Step 1: Since 521 > 343, we apply the division lemma to 521 and 343, to get

521 = 343 x 1 + 178

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 178 and 343, to get

343 = 178 x 1 + 165

Step 3: We consider the new divisor 178 and the new remainder 165, and apply the division lemma to get

178 = 165 x 1 + 13

We consider the new divisor 165 and the new remainder 13,and apply the division lemma to get

165 = 13 x 12 + 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 521 and 343 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(165,13) = HCF(178,165) = HCF(343,178) = HCF(521,343) .

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Frequently Asked Questions on HCF of 521, 343 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 521, 343?

Answer: HCF of 521, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 521, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 521, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.