Highest Common Factor of 663, 894, 380 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 663, 894, 380 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 894, 380 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 663, 894, 380 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 663, 894, 380 is 1.

HCF(663, 894, 380) = 1

HCF of 663, 894, 380 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 663, 894, 380 is 1.

Highest Common Factor of 663,894,380 using Euclid's algorithm

Highest Common Factor of 663,894,380 is 1

Step 1: Since 894 > 663, we apply the division lemma to 894 and 663, to get

894 = 663 x 1 + 231

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 231 and 663, to get

663 = 231 x 2 + 201

Step 3: We consider the new divisor 231 and the new remainder 201, and apply the division lemma to get

231 = 201 x 1 + 30

We consider the new divisor 201 and the new remainder 30,and apply the division lemma to get

201 = 30 x 6 + 21

We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get

30 = 21 x 1 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 663 and 894 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(201,30) = HCF(231,201) = HCF(663,231) = HCF(894,663) .

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

Step 1: Since 380 > 3, we apply the division lemma to 380 and 3, to get

380 = 3 x 126 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 380 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(380,3) .

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Frequently Asked Questions on HCF of 663, 894, 380 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 663, 894, 380?

Answer: HCF of 663, 894, 380 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 894, 380 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 894, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.