Highest Common Factor of 512, 609, 261 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, 609, 261 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 609, 261 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, 609, 261 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, 609, 261 is 1.

HCF(512, 609, 261) = 1

HCF of 512, 609, 261 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, 609, 261 is 1.

Highest Common Factor of 512,609,261 using Euclid's algorithm

Highest Common Factor of 512,609,261 is 1

Step 1: Since 609 > 512, we apply the division lemma to 609 and 512, to get

609 = 512 x 1 + 97

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 97 and 512, to get

512 = 97 x 5 + 27

Step 3: We consider the new divisor 97 and the new remainder 27, and apply the division lemma to get

97 = 27 x 3 + 16

We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get

27 = 16 x 1 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 512 and 609 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(97,27) = HCF(512,97) = HCF(609,512) .

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

Step 1: Since 261 > 1, we apply the division lemma to 261 and 1, to get

261 = 1 x 261 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 261 is 1

Notice that 1 = HCF(261,1) .

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Frequently Asked Questions on HCF of 512, 609, 261 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, 609, 261?

Answer: HCF of 512, 609, 261 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 609, 261 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 609, 261 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.