Highest Common Factor of 273, 923, 117 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 273, 923, 117 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 273, 923, 117 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 273, 923, 117 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 273, 923, 117 is 13.

HCF(273, 923, 117) = 13

HCF of 273, 923, 117 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 273, 923, 117 is 13.

Highest Common Factor of 273,923,117 using Euclid's algorithm

Highest Common Factor of 273,923,117 is 13

Step 1: Since 923 > 273, we apply the division lemma to 923 and 273, to get

923 = 273 x 3 + 104

Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 104 and 273, to get

273 = 104 x 2 + 65

Step 3: We consider the new divisor 104 and the new remainder 65, and apply the division lemma to get

104 = 65 x 1 + 39

We consider the new divisor 65 and the new remainder 39,and apply the division lemma to get

65 = 39 x 1 + 26

We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get

39 = 26 x 1 + 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 273 and 923 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(104,65) = HCF(273,104) = HCF(923,273) .

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

Step 1: Since 117 > 13, we apply the division lemma to 117 and 13, to get

117 = 13 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 117 is 13

Notice that 13 = HCF(117,13) .

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Frequently Asked Questions on HCF of 273, 923, 117 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 273, 923, 117?

Answer: HCF of 273, 923, 117 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 273, 923, 117 using Euclid's Algorithm?

Answer: For arbitrary numbers 273, 923, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.