Highest Common Factor of 663, 512 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 663, 512 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 512 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 663, 512 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 663, 512 is 1.

HCF(663, 512) = 1

HCF of 663, 512 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 663, 512 is 1.

Highest Common Factor of 663,512 using Euclid's algorithm

Highest Common Factor of 663,512 is 1

Step 1: Since 663 > 512, we apply the division lemma to 663 and 512, to get

663 = 512 x 1 + 151

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 151 and 512, to get

512 = 151 x 3 + 59

Step 3: We consider the new divisor 151 and the new remainder 59, and apply the division lemma to get

151 = 59 x 2 + 33

We consider the new divisor 59 and the new remainder 33,and apply the division lemma to get

59 = 33 x 1 + 26

We consider the new divisor 33 and the new remainder 26,and apply the division lemma to get

33 = 26 x 1 + 7

We consider the new divisor 26 and the new remainder 7,and apply the division lemma to get

26 = 7 x 3 + 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 663 and 512 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(26,7) = HCF(33,26) = HCF(59,33) = HCF(151,59) = HCF(512,151) = HCF(663,512) .

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Frequently Asked Questions on HCF of 663, 512 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 663, 512?

Answer: HCF of 663, 512 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 512 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.