Highest Common Factor of 585, 923, 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 585, 923, 273 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 923, 273 is 13 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 585, 923, 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 585, 923, 273 is 13.

HCF(585, 923, 273) = 13

HCF of 585, 923, 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 585, 923, 273 is 13.

Highest Common Factor of 585,923,273 using Euclid's algorithm

Highest Common Factor of 585,923,273 is 13

Step 1: Since 923 > 585, we apply the division lemma to 923 and 585, to get

923 = 585 x 1 + 338

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 338 and 585, to get

585 = 338 x 1 + 247

Step 3: We consider the new divisor 338 and the new remainder 247, and apply the division lemma to get

338 = 247 x 1 + 91

We consider the new divisor 247 and the new remainder 91,and apply the division lemma to get

247 = 91 x 2 + 65

We consider the new divisor 91 and the new remainder 65,and apply the division lemma to get

91 = 65 x 1 + 26

We consider the new divisor 65 and the new remainder 26,and apply the division lemma to get

65 = 26 x 2 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 585 and 923 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(91,65) = HCF(247,91) = HCF(338,247) = HCF(585,338) = HCF(923,585) .

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

Step 1: Since 273 > 13, we apply the division lemma to 273 and 13, to get

273 = 13 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 273 is 13

Notice that 13 = HCF(273,13) .

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Frequently Asked Questions on HCF of 585, 923, 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 585, 923, 273?

Answer: HCF of 585, 923, 273 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 923, 273 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 923, 273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.