Highest Common Factor of 9071, 2685, 42102 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 9071, 2685, 42102 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9071, 2685, 42102 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 9071, 2685, 42102 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 9071, 2685, 42102 is 1.

HCF(9071, 2685, 42102) = 1

HCF of 9071, 2685, 42102 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 9071, 2685, 42102 is 1.

Highest Common Factor of 9071,2685,42102 using Euclid's algorithm

Highest Common Factor of 9071,2685,42102 is 1

Step 1: Since 9071 > 2685, we apply the division lemma to 9071 and 2685, to get

9071 = 2685 x 3 + 1016

Step 2: Since the reminder 2685 ≠ 0, we apply division lemma to 1016 and 2685, to get

2685 = 1016 x 2 + 653

Step 3: We consider the new divisor 1016 and the new remainder 653, and apply the division lemma to get

1016 = 653 x 1 + 363

We consider the new divisor 653 and the new remainder 363,and apply the division lemma to get

653 = 363 x 1 + 290

We consider the new divisor 363 and the new remainder 290,and apply the division lemma to get

363 = 290 x 1 + 73

We consider the new divisor 290 and the new remainder 73,and apply the division lemma to get

290 = 73 x 3 + 71

We consider the new divisor 73 and the new remainder 71,and apply the division lemma to get

73 = 71 x 1 + 2

We consider the new divisor 71 and the new remainder 2,and apply the division lemma to get

71 = 2 x 35 + 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 9071 and 2685 is 1

Notice that 1 = HCF(2,1) = HCF(71,2) = HCF(73,71) = HCF(290,73) = HCF(363,290) = HCF(653,363) = HCF(1016,653) = HCF(2685,1016) = HCF(9071,2685) .

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

Step 1: Since 42102 > 1, we apply the division lemma to 42102 and 1, to get

42102 = 1 x 42102 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42102 is 1

Notice that 1 = HCF(42102,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 9071, 2685, 42102 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 9071, 2685, 42102?

Answer: HCF of 9071, 2685, 42102 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9071, 2685, 42102 using Euclid's Algorithm?

Answer: For arbitrary numbers 9071, 2685, 42102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.