Highest Common Factor of 282, 6982, 3687 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 282, 6982, 3687 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 282, 6982, 3687 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 282, 6982, 3687 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 282, 6982, 3687 is 1.

HCF(282, 6982, 3687) = 1

HCF of 282, 6982, 3687 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 282, 6982, 3687 is 1.

Highest Common Factor of 282,6982,3687 using Euclid's algorithm

Highest Common Factor of 282,6982,3687 is 1

Step 1: Since 6982 > 282, we apply the division lemma to 6982 and 282, to get

6982 = 282 x 24 + 214

Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 214 and 282, to get

282 = 214 x 1 + 68

Step 3: We consider the new divisor 214 and the new remainder 68, and apply the division lemma to get

214 = 68 x 3 + 10

We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get

68 = 10 x 6 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 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 282 and 6982 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(214,68) = HCF(282,214) = HCF(6982,282) .

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

Step 1: Since 3687 > 2, we apply the division lemma to 3687 and 2, to get

3687 = 2 x 1843 + 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 3687 is 1

Notice that 1 = HCF(2,1) = HCF(3687,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 282, 6982, 3687 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 282, 6982, 3687?

Answer: HCF of 282, 6982, 3687 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 282, 6982, 3687 using Euclid's Algorithm?

Answer: For arbitrary numbers 282, 6982, 3687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.