Highest Common Factor of 514, 321, 363 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 514, 321, 363 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 321, 363 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 514, 321, 363 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 514, 321, 363 is 1.

HCF(514, 321, 363) = 1

HCF of 514, 321, 363 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 514, 321, 363 is 1.

Highest Common Factor of 514,321,363 using Euclid's algorithm

Highest Common Factor of 514,321,363 is 1

Step 1: Since 514 > 321, we apply the division lemma to 514 and 321, to get

514 = 321 x 1 + 193

Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 193 and 321, to get

321 = 193 x 1 + 128

Step 3: We consider the new divisor 193 and the new remainder 128, and apply the division lemma to get

193 = 128 x 1 + 65

We consider the new divisor 128 and the new remainder 65,and apply the division lemma to get

128 = 65 x 1 + 63

We consider the new divisor 65 and the new remainder 63,and apply the division lemma to get

65 = 63 x 1 + 2

We consider the new divisor 63 and the new remainder 2,and apply the division lemma to get

63 = 2 x 31 + 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 514 and 321 is 1

Notice that 1 = HCF(2,1) = HCF(63,2) = HCF(65,63) = HCF(128,65) = HCF(193,128) = HCF(321,193) = HCF(514,321) .

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

Step 1: Since 363 > 1, we apply the division lemma to 363 and 1, to get

363 = 1 x 363 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 363 is 1

Notice that 1 = HCF(363,1) .

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Frequently Asked Questions on HCF of 514, 321, 363 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 514, 321, 363?

Answer: HCF of 514, 321, 363 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 321, 363 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 321, 363 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.