Highest Common Factor of 366, 309, 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 366, 309, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 366, 309, 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 366, 309, 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 366, 309, 343 is 1.

HCF(366, 309, 343) = 1

HCF of 366, 309, 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 366, 309, 343 is 1.

Highest Common Factor of 366,309,343 using Euclid's algorithm

Highest Common Factor of 366,309,343 is 1

Step 1: Since 366 > 309, we apply the division lemma to 366 and 309, to get

366 = 309 x 1 + 57

Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 57 and 309, to get

309 = 57 x 5 + 24

Step 3: We consider the new divisor 57 and the new remainder 24, and apply the division lemma to get

57 = 24 x 2 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 366 and 309 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(309,57) = HCF(366,309) .

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

Step 1: Since 343 > 3, we apply the division lemma to 343 and 3, to get

343 = 3 x 114 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 343 is 1

Notice that 1 = HCF(3,1) = HCF(343,3) .

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Frequently Asked Questions on HCF of 366, 309, 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 366, 309, 343?

Answer: HCF of 366, 309, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 366, 309, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 366, 309, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.