Highest Common Factor of 7173, 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 7173, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7173, 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 7173, 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 7173, 343 is 1.

HCF(7173, 343) = 1

HCF of 7173, 343 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 7173, 343 is 1.

Highest Common Factor of 7173,343 using Euclid's algorithm

Highest Common Factor of 7173,343 is 1

Step 1: Since 7173 > 343, we apply the division lemma to 7173 and 343, to get

7173 = 343 x 20 + 313

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 313 and 343, to get

343 = 313 x 1 + 30

Step 3: We consider the new divisor 313 and the new remainder 30, and apply the division lemma to get

313 = 30 x 10 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 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 7173 and 343 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(313,30) = HCF(343,313) = HCF(7173,343) .

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Frequently Asked Questions on HCF of 7173, 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 7173, 343?

Answer: HCF of 7173, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7173, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 7173, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.