Highest Common Factor of 768, 667, 387 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 768, 667, 387 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 768, 667, 387 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 768, 667, 387 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 768, 667, 387 is 1.

HCF(768, 667, 387) = 1

HCF of 768, 667, 387 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 768, 667, 387 is 1.

Highest Common Factor of 768,667,387 using Euclid's algorithm

Highest Common Factor of 768,667,387 is 1

Step 1: Since 768 > 667, we apply the division lemma to 768 and 667, to get

768 = 667 x 1 + 101

Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 101 and 667, to get

667 = 101 x 6 + 61

Step 3: We consider the new divisor 101 and the new remainder 61, and apply the division lemma to get

101 = 61 x 1 + 40

We consider the new divisor 61 and the new remainder 40,and apply the division lemma to get

61 = 40 x 1 + 21

We consider the new divisor 40 and the new remainder 21,and apply the division lemma to get

40 = 21 x 1 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

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 768 and 667 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(61,40) = HCF(101,61) = HCF(667,101) = HCF(768,667) .

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

Step 1: Since 387 > 1, we apply the division lemma to 387 and 1, to get

387 = 1 x 387 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 387 is 1

Notice that 1 = HCF(387,1) .

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Frequently Asked Questions on HCF of 768, 667, 387 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 768, 667, 387?

Answer: HCF of 768, 667, 387 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 768, 667, 387 using Euclid's Algorithm?

Answer: For arbitrary numbers 768, 667, 387 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.