Highest Common Factor of 343, 407 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 343, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 407 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 343, 407 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 343, 407 is 1.

HCF(343, 407) = 1

HCF of 343, 407 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 343, 407 is 1.

Highest Common Factor of 343,407 using Euclid's algorithm

Highest Common Factor of 343,407 is 1

Step 1: Since 407 > 343, we apply the division lemma to 407 and 343, to get

407 = 343 x 1 + 64

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 64 and 343, to get

343 = 64 x 5 + 23

Step 3: We consider the new divisor 64 and the new remainder 23, and apply the division lemma to get

64 = 23 x 2 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 343 and 407 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(64,23) = HCF(343,64) = HCF(407,343) .

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Frequently Asked Questions on HCF of 343, 407 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 343, 407?

Answer: HCF of 343, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 407 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.