Highest Common Factor of 9142, 8912, 85867 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 9142, 8912, 85867 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9142, 8912, 85867 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 9142, 8912, 85867 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 9142, 8912, 85867 is 1.

HCF(9142, 8912, 85867) = 1

HCF of 9142, 8912, 85867 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 9142, 8912, 85867 is 1.

Highest Common Factor of 9142,8912,85867 using Euclid's algorithm

Highest Common Factor of 9142,8912,85867 is 1

Step 1: Since 9142 > 8912, we apply the division lemma to 9142 and 8912, to get

9142 = 8912 x 1 + 230

Step 2: Since the reminder 8912 ≠ 0, we apply division lemma to 230 and 8912, to get

8912 = 230 x 38 + 172

Step 3: We consider the new divisor 230 and the new remainder 172, and apply the division lemma to get

230 = 172 x 1 + 58

We consider the new divisor 172 and the new remainder 58,and apply the division lemma to get

172 = 58 x 2 + 56

We consider the new divisor 58 and the new remainder 56,and apply the division lemma to get

58 = 56 x 1 + 2

We consider the new divisor 56 and the new remainder 2,and apply the division lemma to get

56 = 2 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9142 and 8912 is 2

Notice that 2 = HCF(56,2) = HCF(58,56) = HCF(172,58) = HCF(230,172) = HCF(8912,230) = HCF(9142,8912) .

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

Step 1: Since 85867 > 2, we apply the division lemma to 85867 and 2, to get

85867 = 2 x 42933 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 85867 is 1

Notice that 1 = HCF(2,1) = HCF(85867,2) .

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Frequently Asked Questions on HCF of 9142, 8912, 85867 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 9142, 8912, 85867?

Answer: HCF of 9142, 8912, 85867 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9142, 8912, 85867 using Euclid's Algorithm?

Answer: For arbitrary numbers 9142, 8912, 85867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.