Highest Common Factor of 273, 696, 474 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, 696, 474 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 273, 696, 474 is 3 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, 696, 474 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, 696, 474 is 3.

HCF(273, 696, 474) = 3

HCF of 273, 696, 474 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, 696, 474 is 3.

Highest Common Factor of 273,696,474 using Euclid's algorithm

Highest Common Factor of 273,696,474 is 3

Step 1: Since 696 > 273, we apply the division lemma to 696 and 273, to get

696 = 273 x 2 + 150

Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 150 and 273, to get

273 = 150 x 1 + 123

Step 3: We consider the new divisor 150 and the new remainder 123, and apply the division lemma to get

150 = 123 x 1 + 27

We consider the new divisor 123 and the new remainder 27,and apply the division lemma to get

123 = 27 x 4 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 273 and 696 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(123,27) = HCF(150,123) = HCF(273,150) = HCF(696,273) .

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

Step 1: Since 474 > 3, we apply the division lemma to 474 and 3, to get

474 = 3 x 158 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 474 is 3

Notice that 3 = HCF(474,3) .

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Frequently Asked Questions on HCF of 273, 696, 474 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, 696, 474?

Answer: HCF of 273, 696, 474 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 273, 696, 474 using Euclid's Algorithm?

Answer: For arbitrary numbers 273, 696, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.