Highest Common Factor of 2035, 8688 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 2035, 8688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2035, 8688 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 2035, 8688 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 2035, 8688 is 1.

HCF(2035, 8688) = 1

HCF of 2035, 8688 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 2035, 8688 is 1.

Highest Common Factor of 2035,8688 using Euclid's algorithm

Highest Common Factor of 2035,8688 is 1

Step 1: Since 8688 > 2035, we apply the division lemma to 8688 and 2035, to get

8688 = 2035 x 4 + 548

Step 2: Since the reminder 2035 ≠ 0, we apply division lemma to 548 and 2035, to get

2035 = 548 x 3 + 391

Step 3: We consider the new divisor 548 and the new remainder 391, and apply the division lemma to get

548 = 391 x 1 + 157

We consider the new divisor 391 and the new remainder 157,and apply the division lemma to get

391 = 157 x 2 + 77

We consider the new divisor 157 and the new remainder 77,and apply the division lemma to get

157 = 77 x 2 + 3

We consider the new divisor 77 and the new remainder 3,and apply the division lemma to get

77 = 3 x 25 + 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 2035 and 8688 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(77,3) = HCF(157,77) = HCF(391,157) = HCF(548,391) = HCF(2035,548) = HCF(8688,2035) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 2035, 8688 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 2035, 8688?

Answer: HCF of 2035, 8688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2035, 8688 using Euclid's Algorithm?

Answer: For arbitrary numbers 2035, 8688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.