Highest Common Factor of 9605, 6754 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 9605, 6754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9605, 6754 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 9605, 6754 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 9605, 6754 is 1.

HCF(9605, 6754) = 1

HCF of 9605, 6754 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 9605, 6754 is 1.

Highest Common Factor of 9605,6754 using Euclid's algorithm

Highest Common Factor of 9605,6754 is 1

Step 1: Since 9605 > 6754, we apply the division lemma to 9605 and 6754, to get

9605 = 6754 x 1 + 2851

Step 2: Since the reminder 6754 ≠ 0, we apply division lemma to 2851 and 6754, to get

6754 = 2851 x 2 + 1052

Step 3: We consider the new divisor 2851 and the new remainder 1052, and apply the division lemma to get

2851 = 1052 x 2 + 747

We consider the new divisor 1052 and the new remainder 747,and apply the division lemma to get

1052 = 747 x 1 + 305

We consider the new divisor 747 and the new remainder 305,and apply the division lemma to get

747 = 305 x 2 + 137

We consider the new divisor 305 and the new remainder 137,and apply the division lemma to get

305 = 137 x 2 + 31

We consider the new divisor 137 and the new remainder 31,and apply the division lemma to get

137 = 31 x 4 + 13

We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get

31 = 13 x 2 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

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 9605 and 6754 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(137,31) = HCF(305,137) = HCF(747,305) = HCF(1052,747) = HCF(2851,1052) = HCF(6754,2851) = HCF(9605,6754) .

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Frequently Asked Questions on HCF of 9605, 6754 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 9605, 6754?

Answer: HCF of 9605, 6754 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9605, 6754 using Euclid's Algorithm?

Answer: For arbitrary numbers 9605, 6754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.