Highest Common Factor of 549, 344, 311 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 549, 344, 311 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 549, 344, 311 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 549, 344, 311 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 549, 344, 311 is 1.

HCF(549, 344, 311) = 1

HCF of 549, 344, 311 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 549, 344, 311 is 1.

Highest Common Factor of 549,344,311 using Euclid's algorithm

Highest Common Factor of 549,344,311 is 1

Step 1: Since 549 > 344, we apply the division lemma to 549 and 344, to get

549 = 344 x 1 + 205

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 205 and 344, to get

344 = 205 x 1 + 139

Step 3: We consider the new divisor 205 and the new remainder 139, and apply the division lemma to get

205 = 139 x 1 + 66

We consider the new divisor 139 and the new remainder 66,and apply the division lemma to get

139 = 66 x 2 + 7

We consider the new divisor 66 and the new remainder 7,and apply the division lemma to get

66 = 7 x 9 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 549 and 344 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(66,7) = HCF(139,66) = HCF(205,139) = HCF(344,205) = HCF(549,344) .

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

Step 1: Since 311 > 1, we apply the division lemma to 311 and 1, to get

311 = 1 x 311 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 311 is 1

Notice that 1 = HCF(311,1) .

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Frequently Asked Questions on HCF of 549, 344, 311 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 549, 344, 311?

Answer: HCF of 549, 344, 311 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 549, 344, 311 using Euclid's Algorithm?

Answer: For arbitrary numbers 549, 344, 311 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.