Highest Common Factor of 9709, 3275, 97164 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 9709, 3275, 97164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9709, 3275, 97164 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 9709, 3275, 97164 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 9709, 3275, 97164 is 1.

HCF(9709, 3275, 97164) = 1

HCF of 9709, 3275, 97164 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 9709, 3275, 97164 is 1.

Highest Common Factor of 9709,3275,97164 using Euclid's algorithm

Highest Common Factor of 9709,3275,97164 is 1

Step 1: Since 9709 > 3275, we apply the division lemma to 9709 and 3275, to get

9709 = 3275 x 2 + 3159

Step 2: Since the reminder 3275 ≠ 0, we apply division lemma to 3159 and 3275, to get

3275 = 3159 x 1 + 116

Step 3: We consider the new divisor 3159 and the new remainder 116, and apply the division lemma to get

3159 = 116 x 27 + 27

We consider the new divisor 116 and the new remainder 27,and apply the division lemma to get

116 = 27 x 4 + 8

We consider the new divisor 27 and the new remainder 8,and apply the division lemma to get

27 = 8 x 3 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 9709 and 3275 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(27,8) = HCF(116,27) = HCF(3159,116) = HCF(3275,3159) = HCF(9709,3275) .

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

Step 1: Since 97164 > 1, we apply the division lemma to 97164 and 1, to get

97164 = 1 x 97164 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 97164 is 1

Notice that 1 = HCF(97164,1) .

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Frequently Asked Questions on HCF of 9709, 3275, 97164 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 9709, 3275, 97164?

Answer: HCF of 9709, 3275, 97164 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9709, 3275, 97164 using Euclid's Algorithm?

Answer: For arbitrary numbers 9709, 3275, 97164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.