Highest Common Factor of 512, 960, 273 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, 960, 273 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 960, 273 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, 960, 273 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, 960, 273 is 1.

HCF(512, 960, 273) = 1

HCF of 512, 960, 273 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, 960, 273 is 1.

Highest Common Factor of 512,960,273 using Euclid's algorithm

Highest Common Factor of 512,960,273 is 1

Step 1: Since 960 > 512, we apply the division lemma to 960 and 512, to get

960 = 512 x 1 + 448

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 448 and 512, to get

512 = 448 x 1 + 64

Step 3: We consider the new divisor 448 and the new remainder 64, and apply the division lemma to get

448 = 64 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 64, the HCF of 512 and 960 is 64

Notice that 64 = HCF(448,64) = HCF(512,448) = HCF(960,512) .

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

Step 1: Since 273 > 64, we apply the division lemma to 273 and 64, to get

273 = 64 x 4 + 17

Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 17 and 64, to get

64 = 17 x 3 + 13

Step 3: We consider the new divisor 17 and the new remainder 13, and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 64 and 273 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(64,17) = HCF(273,64) .

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Frequently Asked Questions on HCF of 512, 960, 273 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, 960, 273?

Answer: HCF of 512, 960, 273 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 960, 273 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 960, 273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.