Highest Common Factor of 897, 3282, 2270 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 897, 3282, 2270 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 897, 3282, 2270 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 897, 3282, 2270 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 897, 3282, 2270 is 1.

HCF(897, 3282, 2270) = 1

HCF of 897, 3282, 2270 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 897, 3282, 2270 is 1.

Highest Common Factor of 897,3282,2270 using Euclid's algorithm

Highest Common Factor of 897,3282,2270 is 1

Step 1: Since 3282 > 897, we apply the division lemma to 3282 and 897, to get

3282 = 897 x 3 + 591

Step 2: Since the reminder 897 ≠ 0, we apply division lemma to 591 and 897, to get

897 = 591 x 1 + 306

Step 3: We consider the new divisor 591 and the new remainder 306, and apply the division lemma to get

591 = 306 x 1 + 285

We consider the new divisor 306 and the new remainder 285,and apply the division lemma to get

306 = 285 x 1 + 21

We consider the new divisor 285 and the new remainder 21,and apply the division lemma to get

285 = 21 x 13 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 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 897 and 3282 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(285,21) = HCF(306,285) = HCF(591,306) = HCF(897,591) = HCF(3282,897) .

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

Step 1: Since 2270 > 3, we apply the division lemma to 2270 and 3, to get

2270 = 3 x 756 + 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 2270 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(2270,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 897, 3282, 2270 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 897, 3282, 2270?

Answer: HCF of 897, 3282, 2270 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 897, 3282, 2270 using Euclid's Algorithm?

Answer: For arbitrary numbers 897, 3282, 2270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.