Highest Common Factor of 309, 514, 443 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 309, 514, 443 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 309, 514, 443 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 309, 514, 443 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 309, 514, 443 is 1.

HCF(309, 514, 443) = 1

HCF of 309, 514, 443 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 309, 514, 443 is 1.

Highest Common Factor of 309,514,443 using Euclid's algorithm

Highest Common Factor of 309,514,443 is 1

Step 1: Since 514 > 309, we apply the division lemma to 514 and 309, to get

514 = 309 x 1 + 205

Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 205 and 309, to get

309 = 205 x 1 + 104

Step 3: We consider the new divisor 205 and the new remainder 104, and apply the division lemma to get

205 = 104 x 1 + 101

We consider the new divisor 104 and the new remainder 101,and apply the division lemma to get

104 = 101 x 1 + 3

We consider the new divisor 101 and the new remainder 3,and apply the division lemma to get

101 = 3 x 33 + 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 309 and 514 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(101,3) = HCF(104,101) = HCF(205,104) = HCF(309,205) = HCF(514,309) .

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

Step 1: Since 443 > 1, we apply the division lemma to 443 and 1, to get

443 = 1 x 443 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 443 is 1

Notice that 1 = HCF(443,1) .

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Frequently Asked Questions on HCF of 309, 514, 443 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 309, 514, 443?

Answer: HCF of 309, 514, 443 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 309, 514, 443 using Euclid's Algorithm?

Answer: For arbitrary numbers 309, 514, 443 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.