Highest Common Factor of 6815, 2970, 68707 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 6815, 2970, 68707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6815, 2970, 68707 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 6815, 2970, 68707 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 6815, 2970, 68707 is 1.

HCF(6815, 2970, 68707) = 1

HCF of 6815, 2970, 68707 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 6815, 2970, 68707 is 1.

Highest Common Factor of 6815,2970,68707 using Euclid's algorithm

Highest Common Factor of 6815,2970,68707 is 1

Step 1: Since 6815 > 2970, we apply the division lemma to 6815 and 2970, to get

6815 = 2970 x 2 + 875

Step 2: Since the reminder 2970 ≠ 0, we apply division lemma to 875 and 2970, to get

2970 = 875 x 3 + 345

Step 3: We consider the new divisor 875 and the new remainder 345, and apply the division lemma to get

875 = 345 x 2 + 185

We consider the new divisor 345 and the new remainder 185,and apply the division lemma to get

345 = 185 x 1 + 160

We consider the new divisor 185 and the new remainder 160,and apply the division lemma to get

185 = 160 x 1 + 25

We consider the new divisor 160 and the new remainder 25,and apply the division lemma to get

160 = 25 x 6 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6815 and 2970 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(160,25) = HCF(185,160) = HCF(345,185) = HCF(875,345) = HCF(2970,875) = HCF(6815,2970) .

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

Step 1: Since 68707 > 5, we apply the division lemma to 68707 and 5, to get

68707 = 5 x 13741 + 2

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

5 = 2 x 2 + 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 5 and 68707 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(68707,5) .

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Frequently Asked Questions on HCF of 6815, 2970, 68707 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 6815, 2970, 68707?

Answer: HCF of 6815, 2970, 68707 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6815, 2970, 68707 using Euclid's Algorithm?

Answer: For arbitrary numbers 6815, 2970, 68707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.