Highest Common Factor of 563, 348, 321 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 563, 348, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 563, 348, 321 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 563, 348, 321 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 563, 348, 321 is 1.

HCF(563, 348, 321) = 1

HCF of 563, 348, 321 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 563, 348, 321 is 1.

Highest Common Factor of 563,348,321 using Euclid's algorithm

Highest Common Factor of 563,348,321 is 1

Step 1: Since 563 > 348, we apply the division lemma to 563 and 348, to get

563 = 348 x 1 + 215

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 215 and 348, to get

348 = 215 x 1 + 133

Step 3: We consider the new divisor 215 and the new remainder 133, and apply the division lemma to get

215 = 133 x 1 + 82

We consider the new divisor 133 and the new remainder 82,and apply the division lemma to get

133 = 82 x 1 + 51

We consider the new divisor 82 and the new remainder 51,and apply the division lemma to get

82 = 51 x 1 + 31

We consider the new divisor 51 and the new remainder 31,and apply the division lemma to get

51 = 31 x 1 + 20

We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get

31 = 20 x 1 + 11

We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get

20 = 11 x 1 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 563 and 348 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(51,31) = HCF(82,51) = HCF(133,82) = HCF(215,133) = HCF(348,215) = HCF(563,348) .

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

Step 1: Since 321 > 1, we apply the division lemma to 321 and 1, to get

321 = 1 x 321 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 321 is 1

Notice that 1 = HCF(321,1) .

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Frequently Asked Questions on HCF of 563, 348, 321 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 563, 348, 321?

Answer: HCF of 563, 348, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 563, 348, 321 using Euclid's Algorithm?

Answer: For arbitrary numbers 563, 348, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.