Highest Common Factor of 2032, 6965 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 2032, 6965 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2032, 6965 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 2032, 6965 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 2032, 6965 is 1.

HCF(2032, 6965) = 1

HCF of 2032, 6965 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 2032, 6965 is 1.

Highest Common Factor of 2032,6965 using Euclid's algorithm

Highest Common Factor of 2032,6965 is 1

Step 1: Since 6965 > 2032, we apply the division lemma to 6965 and 2032, to get

6965 = 2032 x 3 + 869

Step 2: Since the reminder 2032 ≠ 0, we apply division lemma to 869 and 2032, to get

2032 = 869 x 2 + 294

Step 3: We consider the new divisor 869 and the new remainder 294, and apply the division lemma to get

869 = 294 x 2 + 281

We consider the new divisor 294 and the new remainder 281,and apply the division lemma to get

294 = 281 x 1 + 13

We consider the new divisor 281 and the new remainder 13,and apply the division lemma to get

281 = 13 x 21 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 2032 and 6965 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(281,13) = HCF(294,281) = HCF(869,294) = HCF(2032,869) = HCF(6965,2032) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 2032, 6965 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 2032, 6965?

Answer: HCF of 2032, 6965 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2032, 6965 using Euclid's Algorithm?

Answer: For arbitrary numbers 2032, 6965 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.