Highest Common Factor of 768, 1930, 3345 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, 1930, 3345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 768, 1930, 3345 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, 1930, 3345 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, 1930, 3345 is 1.

HCF(768, 1930, 3345) = 1

HCF of 768, 1930, 3345 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, 1930, 3345 is 1.

Highest Common Factor of 768,1930,3345 using Euclid's algorithm

Highest Common Factor of 768,1930,3345 is 1

Step 1: Since 1930 > 768, we apply the division lemma to 1930 and 768, to get

1930 = 768 x 2 + 394

Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 394 and 768, to get

768 = 394 x 1 + 374

Step 3: We consider the new divisor 394 and the new remainder 374, and apply the division lemma to get

394 = 374 x 1 + 20

We consider the new divisor 374 and the new remainder 20,and apply the division lemma to get

374 = 20 x 18 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 768 and 1930 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(374,20) = HCF(394,374) = HCF(768,394) = HCF(1930,768) .

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

Step 1: Since 3345 > 2, we apply the division lemma to 3345 and 2, to get

3345 = 2 x 1672 + 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 3345 is 1

Notice that 1 = HCF(2,1) = HCF(3345,2) .

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Frequently Asked Questions on HCF of 768, 1930, 3345 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, 1930, 3345?

Answer: HCF of 768, 1930, 3345 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 768, 1930, 3345 using Euclid's Algorithm?

Answer: For arbitrary numbers 768, 1930, 3345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.