Highest Common Factor of 463, 768, 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 463, 768, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 463, 768, 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 463, 768, 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 463, 768, 321 is 1.

HCF(463, 768, 321) = 1

HCF of 463, 768, 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 463, 768, 321 is 1.

Highest Common Factor of 463,768,321 using Euclid's algorithm

Highest Common Factor of 463,768,321 is 1

Step 1: Since 768 > 463, we apply the division lemma to 768 and 463, to get

768 = 463 x 1 + 305

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 305 and 463, to get

463 = 305 x 1 + 158

Step 3: We consider the new divisor 305 and the new remainder 158, and apply the division lemma to get

305 = 158 x 1 + 147

We consider the new divisor 158 and the new remainder 147,and apply the division lemma to get

158 = 147 x 1 + 11

We consider the new divisor 147 and the new remainder 11,and apply the division lemma to get

147 = 11 x 13 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 463 and 768 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(147,11) = HCF(158,147) = HCF(305,158) = HCF(463,305) = HCF(768,463) .

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 463, 768, 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 463, 768, 321?

Answer: HCF of 463, 768, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 463, 768, 321 using Euclid's Algorithm?

Answer: For arbitrary numbers 463, 768, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.