Highest Common Factor of 6837, 9835, 20705 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 6837, 9835, 20705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6837, 9835, 20705 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 6837, 9835, 20705 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 6837, 9835, 20705 is 1.

HCF(6837, 9835, 20705) = 1

HCF of 6837, 9835, 20705 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 6837, 9835, 20705 is 1.

Highest Common Factor of 6837,9835,20705 using Euclid's algorithm

Highest Common Factor of 6837,9835,20705 is 1

Step 1: Since 9835 > 6837, we apply the division lemma to 9835 and 6837, to get

9835 = 6837 x 1 + 2998

Step 2: Since the reminder 6837 ≠ 0, we apply division lemma to 2998 and 6837, to get

6837 = 2998 x 2 + 841

Step 3: We consider the new divisor 2998 and the new remainder 841, and apply the division lemma to get

2998 = 841 x 3 + 475

We consider the new divisor 841 and the new remainder 475,and apply the division lemma to get

841 = 475 x 1 + 366

We consider the new divisor 475 and the new remainder 366,and apply the division lemma to get

475 = 366 x 1 + 109

We consider the new divisor 366 and the new remainder 109,and apply the division lemma to get

366 = 109 x 3 + 39

We consider the new divisor 109 and the new remainder 39,and apply the division lemma to get

109 = 39 x 2 + 31

We consider the new divisor 39 and the new remainder 31,and apply the division lemma to get

39 = 31 x 1 + 8

We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get

31 = 8 x 3 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6837 and 9835 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(39,31) = HCF(109,39) = HCF(366,109) = HCF(475,366) = HCF(841,475) = HCF(2998,841) = HCF(6837,2998) = HCF(9835,6837) .

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

Step 1: Since 20705 > 1, we apply the division lemma to 20705 and 1, to get

20705 = 1 x 20705 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20705 is 1

Notice that 1 = HCF(20705,1) .

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Frequently Asked Questions on HCF of 6837, 9835, 20705 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 6837, 9835, 20705?

Answer: HCF of 6837, 9835, 20705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6837, 9835, 20705 using Euclid's Algorithm?

Answer: For arbitrary numbers 6837, 9835, 20705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.