Highest Common Factor of 6870, 3538 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 6870, 3538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6870, 3538 is 2 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 6870, 3538 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 6870, 3538 is 2.

HCF(6870, 3538) = 2

HCF of 6870, 3538 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 6870, 3538 is 2.

Highest Common Factor of 6870,3538 using Euclid's algorithm

Highest Common Factor of 6870,3538 is 2

Step 1: Since 6870 > 3538, we apply the division lemma to 6870 and 3538, to get

6870 = 3538 x 1 + 3332

Step 2: Since the reminder 3538 ≠ 0, we apply division lemma to 3332 and 3538, to get

3538 = 3332 x 1 + 206

Step 3: We consider the new divisor 3332 and the new remainder 206, and apply the division lemma to get

3332 = 206 x 16 + 36

We consider the new divisor 206 and the new remainder 36,and apply the division lemma to get

206 = 36 x 5 + 26

We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get

36 = 26 x 1 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6870 and 3538 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(206,36) = HCF(3332,206) = HCF(3538,3332) = HCF(6870,3538) .

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Frequently Asked Questions on HCF of 6870, 3538 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 6870, 3538?

Answer: HCF of 6870, 3538 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6870, 3538 using Euclid's Algorithm?

Answer: For arbitrary numbers 6870, 3538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.