Highest Common Factor of 9606, 6691, 69165 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 9606, 6691, 69165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9606, 6691, 69165 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 9606, 6691, 69165 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 9606, 6691, 69165 is 1.

HCF(9606, 6691, 69165) = 1

HCF of 9606, 6691, 69165 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 9606, 6691, 69165 is 1.

Highest Common Factor of 9606,6691,69165 using Euclid's algorithm

Highest Common Factor of 9606,6691,69165 is 1

Step 1: Since 9606 > 6691, we apply the division lemma to 9606 and 6691, to get

9606 = 6691 x 1 + 2915

Step 2: Since the reminder 6691 ≠ 0, we apply division lemma to 2915 and 6691, to get

6691 = 2915 x 2 + 861

Step 3: We consider the new divisor 2915 and the new remainder 861, and apply the division lemma to get

2915 = 861 x 3 + 332

We consider the new divisor 861 and the new remainder 332,and apply the division lemma to get

861 = 332 x 2 + 197

We consider the new divisor 332 and the new remainder 197,and apply the division lemma to get

332 = 197 x 1 + 135

We consider the new divisor 197 and the new remainder 135,and apply the division lemma to get

197 = 135 x 1 + 62

We consider the new divisor 135 and the new remainder 62,and apply the division lemma to get

135 = 62 x 2 + 11

We consider the new divisor 62 and the new remainder 11,and apply the division lemma to get

62 = 11 x 5 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9606 and 6691 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(62,11) = HCF(135,62) = HCF(197,135) = HCF(332,197) = HCF(861,332) = HCF(2915,861) = HCF(6691,2915) = HCF(9606,6691) .

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

Step 1: Since 69165 > 1, we apply the division lemma to 69165 and 1, to get

69165 = 1 x 69165 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69165 is 1

Notice that 1 = HCF(69165,1) .

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Frequently Asked Questions on HCF of 9606, 6691, 69165 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 9606, 6691, 69165?

Answer: HCF of 9606, 6691, 69165 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9606, 6691, 69165 using Euclid's Algorithm?

Answer: For arbitrary numbers 9606, 6691, 69165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.