Highest Common Factor of 300, 681, 206 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 300, 681, 206 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 300, 681, 206 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 300, 681, 206 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 300, 681, 206 is 1.

HCF(300, 681, 206) = 1

HCF of 300, 681, 206 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 300, 681, 206 is 1.

Highest Common Factor of 300,681,206 using Euclid's algorithm

Highest Common Factor of 300,681,206 is 1

Step 1: Since 681 > 300, we apply the division lemma to 681 and 300, to get

681 = 300 x 2 + 81

Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 81 and 300, to get

300 = 81 x 3 + 57

Step 3: We consider the new divisor 81 and the new remainder 57, and apply the division lemma to get

81 = 57 x 1 + 24

We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get

57 = 24 x 2 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 300 and 681 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(81,57) = HCF(300,81) = HCF(681,300) .

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

Step 1: Since 206 > 3, we apply the division lemma to 206 and 3, to get

206 = 3 x 68 + 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 206 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(206,3) .

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Frequently Asked Questions on HCF of 300, 681, 206 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 300, 681, 206?

Answer: HCF of 300, 681, 206 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 300, 681, 206 using Euclid's Algorithm?

Answer: For arbitrary numbers 300, 681, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.