Highest Common Factor of 768, 7334, 5073 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, 7334, 5073 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 768, 7334, 5073 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, 7334, 5073 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, 7334, 5073 is 1.

HCF(768, 7334, 5073) = 1

HCF of 768, 7334, 5073 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, 7334, 5073 is 1.

Highest Common Factor of 768,7334,5073 using Euclid's algorithm

Highest Common Factor of 768,7334,5073 is 1

Step 1: Since 7334 > 768, we apply the division lemma to 7334 and 768, to get

7334 = 768 x 9 + 422

Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 422 and 768, to get

768 = 422 x 1 + 346

Step 3: We consider the new divisor 422 and the new remainder 346, and apply the division lemma to get

422 = 346 x 1 + 76

We consider the new divisor 346 and the new remainder 76,and apply the division lemma to get

346 = 76 x 4 + 42

We consider the new divisor 76 and the new remainder 42,and apply the division lemma to get

76 = 42 x 1 + 34

We consider the new divisor 42 and the new remainder 34,and apply the division lemma to get

42 = 34 x 1 + 8

We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get

34 = 8 x 4 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 768 and 7334 is 2

Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(42,34) = HCF(76,42) = HCF(346,76) = HCF(422,346) = HCF(768,422) = HCF(7334,768) .

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

Step 1: Since 5073 > 2, we apply the division lemma to 5073 and 2, to get

5073 = 2 x 2536 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 5073 is 1

Notice that 1 = HCF(2,1) = HCF(5073,2) .

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Frequently Asked Questions on HCF of 768, 7334, 5073 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, 7334, 5073?

Answer: HCF of 768, 7334, 5073 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 768, 7334, 5073 using Euclid's Algorithm?

Answer: For arbitrary numbers 768, 7334, 5073 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.