Highest Common Factor of 2032, 7321 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, 7321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2032, 7321 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, 7321 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, 7321 is 1.

HCF(2032, 7321) = 1

HCF of 2032, 7321 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, 7321 is 1.

Highest Common Factor of 2032,7321 using Euclid's algorithm

Highest Common Factor of 2032,7321 is 1

Step 1: Since 7321 > 2032, we apply the division lemma to 7321 and 2032, to get

7321 = 2032 x 3 + 1225

Step 2: Since the reminder 2032 ≠ 0, we apply division lemma to 1225 and 2032, to get

2032 = 1225 x 1 + 807

Step 3: We consider the new divisor 1225 and the new remainder 807, and apply the division lemma to get

1225 = 807 x 1 + 418

We consider the new divisor 807 and the new remainder 418,and apply the division lemma to get

807 = 418 x 1 + 389

We consider the new divisor 418 and the new remainder 389,and apply the division lemma to get

418 = 389 x 1 + 29

We consider the new divisor 389 and the new remainder 29,and apply the division lemma to get

389 = 29 x 13 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 7321 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(389,29) = HCF(418,389) = HCF(807,418) = HCF(1225,807) = HCF(2032,1225) = HCF(7321,2032) .

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Frequently Asked Questions on HCF of 2032, 7321 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, 7321?

Answer: HCF of 2032, 7321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2032, 7321 using Euclid's Algorithm?

Answer: For arbitrary numbers 2032, 7321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.