Highest Common Factor of 661, 273, 382 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 661, 273, 382 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 661, 273, 382 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 661, 273, 382 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 661, 273, 382 is 1.

HCF(661, 273, 382) = 1

HCF of 661, 273, 382 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 661, 273, 382 is 1.

Highest Common Factor of 661,273,382 using Euclid's algorithm

Highest Common Factor of 661,273,382 is 1

Step 1: Since 661 > 273, we apply the division lemma to 661 and 273, to get

661 = 273 x 2 + 115

Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 115 and 273, to get

273 = 115 x 2 + 43

Step 3: We consider the new divisor 115 and the new remainder 43, and apply the division lemma to get

115 = 43 x 2 + 29

We consider the new divisor 43 and the new remainder 29,and apply the division lemma to get

43 = 29 x 1 + 14

We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get

29 = 14 x 2 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 273 is 1

Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(43,29) = HCF(115,43) = HCF(273,115) = HCF(661,273) .

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

Step 1: Since 382 > 1, we apply the division lemma to 382 and 1, to get

382 = 1 x 382 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 382 is 1

Notice that 1 = HCF(382,1) .

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Frequently Asked Questions on HCF of 661, 273, 382 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 661, 273, 382?

Answer: HCF of 661, 273, 382 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 661, 273, 382 using Euclid's Algorithm?

Answer: For arbitrary numbers 661, 273, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.