Highest Common Factor of 9731, 1865, 91432 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 9731, 1865, 91432 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9731, 1865, 91432 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 9731, 1865, 91432 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 9731, 1865, 91432 is 1.

HCF(9731, 1865, 91432) = 1

HCF of 9731, 1865, 91432 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 9731, 1865, 91432 is 1.

Highest Common Factor of 9731,1865,91432 using Euclid's algorithm

Highest Common Factor of 9731,1865,91432 is 1

Step 1: Since 9731 > 1865, we apply the division lemma to 9731 and 1865, to get

9731 = 1865 x 5 + 406

Step 2: Since the reminder 1865 ≠ 0, we apply division lemma to 406 and 1865, to get

1865 = 406 x 4 + 241

Step 3: We consider the new divisor 406 and the new remainder 241, and apply the division lemma to get

406 = 241 x 1 + 165

We consider the new divisor 241 and the new remainder 165,and apply the division lemma to get

241 = 165 x 1 + 76

We consider the new divisor 165 and the new remainder 76,and apply the division lemma to get

165 = 76 x 2 + 13

We consider the new divisor 76 and the new remainder 13,and apply the division lemma to get

76 = 13 x 5 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 9731 and 1865 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(76,13) = HCF(165,76) = HCF(241,165) = HCF(406,241) = HCF(1865,406) = HCF(9731,1865) .

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

Step 1: Since 91432 > 1, we apply the division lemma to 91432 and 1, to get

91432 = 1 x 91432 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 91432 is 1

Notice that 1 = HCF(91432,1) .

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Frequently Asked Questions on HCF of 9731, 1865, 91432 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 9731, 1865, 91432?

Answer: HCF of 9731, 1865, 91432 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9731, 1865, 91432 using Euclid's Algorithm?

Answer: For arbitrary numbers 9731, 1865, 91432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.