Highest Common Factor of 543, 313, 242 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 543, 313, 242 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 543, 313, 242 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 543, 313, 242 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 543, 313, 242 is 1.

HCF(543, 313, 242) = 1

HCF of 543, 313, 242 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 543, 313, 242 is 1.

Highest Common Factor of 543,313,242 using Euclid's algorithm

Highest Common Factor of 543,313,242 is 1

Step 1: Since 543 > 313, we apply the division lemma to 543 and 313, to get

543 = 313 x 1 + 230

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 230 and 313, to get

313 = 230 x 1 + 83

Step 3: We consider the new divisor 230 and the new remainder 83, and apply the division lemma to get

230 = 83 x 2 + 64

We consider the new divisor 83 and the new remainder 64,and apply the division lemma to get

83 = 64 x 1 + 19

We consider the new divisor 64 and the new remainder 19,and apply the division lemma to get

64 = 19 x 3 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 543 and 313 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(64,19) = HCF(83,64) = HCF(230,83) = HCF(313,230) = HCF(543,313) .

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

Step 1: Since 242 > 1, we apply the division lemma to 242 and 1, to get

242 = 1 x 242 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 242 is 1

Notice that 1 = HCF(242,1) .

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Frequently Asked Questions on HCF of 543, 313, 242 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 543, 313, 242?

Answer: HCF of 543, 313, 242 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 543, 313, 242 using Euclid's Algorithm?

Answer: For arbitrary numbers 543, 313, 242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.