Highest Common Factor of 512, 644, 55 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 512, 644, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 644, 55 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 512, 644, 55 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 512, 644, 55 is 1.

HCF(512, 644, 55) = 1

HCF of 512, 644, 55 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 512, 644, 55 is 1.

Highest Common Factor of 512,644,55 using Euclid's algorithm

Highest Common Factor of 512,644,55 is 1

Step 1: Since 644 > 512, we apply the division lemma to 644 and 512, to get

644 = 512 x 1 + 132

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 132 and 512, to get

512 = 132 x 3 + 116

Step 3: We consider the new divisor 132 and the new remainder 116, and apply the division lemma to get

132 = 116 x 1 + 16

We consider the new divisor 116 and the new remainder 16,and apply the division lemma to get

116 = 16 x 7 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 512 and 644 is 4

Notice that 4 = HCF(16,4) = HCF(116,16) = HCF(132,116) = HCF(512,132) = HCF(644,512) .

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

Step 1: Since 55 > 4, we apply the division lemma to 55 and 4, to get

55 = 4 x 13 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 55 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(55,4) .

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Frequently Asked Questions on HCF of 512, 644, 55 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 512, 644, 55?

Answer: HCF of 512, 644, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 644, 55 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 644, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.