Highest Common Factor of 765, 3470, 2966 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 765, 3470, 2966 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 765, 3470, 2966 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 765, 3470, 2966 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 765, 3470, 2966 is 1.

HCF(765, 3470, 2966) = 1

HCF of 765, 3470, 2966 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 765, 3470, 2966 is 1.

Highest Common Factor of 765,3470,2966 using Euclid's algorithm

Highest Common Factor of 765,3470,2966 is 1

Step 1: Since 3470 > 765, we apply the division lemma to 3470 and 765, to get

3470 = 765 x 4 + 410

Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 410 and 765, to get

765 = 410 x 1 + 355

Step 3: We consider the new divisor 410 and the new remainder 355, and apply the division lemma to get

410 = 355 x 1 + 55

We consider the new divisor 355 and the new remainder 55,and apply the division lemma to get

355 = 55 x 6 + 25

We consider the new divisor 55 and the new remainder 25,and apply the division lemma to get

55 = 25 x 2 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 765 and 3470 is 5

Notice that 5 = HCF(25,5) = HCF(55,25) = HCF(355,55) = HCF(410,355) = HCF(765,410) = HCF(3470,765) .

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

Step 1: Since 2966 > 5, we apply the division lemma to 2966 and 5, to get

2966 = 5 x 593 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 2966 is 1

Notice that 1 = HCF(5,1) = HCF(2966,5) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 765, 3470, 2966 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 765, 3470, 2966?

Answer: HCF of 765, 3470, 2966 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 765, 3470, 2966 using Euclid's Algorithm?

Answer: For arbitrary numbers 765, 3470, 2966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.