Highest Common Factor of 8021, 9543 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 8021, 9543 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8021, 9543 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 8021, 9543 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 8021, 9543 is 1.

HCF(8021, 9543) = 1

HCF of 8021, 9543 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 8021, 9543 is 1.

Highest Common Factor of 8021,9543 using Euclid's algorithm

Highest Common Factor of 8021,9543 is 1

Step 1: Since 9543 > 8021, we apply the division lemma to 9543 and 8021, to get

9543 = 8021 x 1 + 1522

Step 2: Since the reminder 8021 ≠ 0, we apply division lemma to 1522 and 8021, to get

8021 = 1522 x 5 + 411

Step 3: We consider the new divisor 1522 and the new remainder 411, and apply the division lemma to get

1522 = 411 x 3 + 289

We consider the new divisor 411 and the new remainder 289,and apply the division lemma to get

411 = 289 x 1 + 122

We consider the new divisor 289 and the new remainder 122,and apply the division lemma to get

289 = 122 x 2 + 45

We consider the new divisor 122 and the new remainder 45,and apply the division lemma to get

122 = 45 x 2 + 32

We consider the new divisor 45 and the new remainder 32,and apply the division lemma to get

45 = 32 x 1 + 13

We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get

32 = 13 x 2 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8021 and 9543 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(122,45) = HCF(289,122) = HCF(411,289) = HCF(1522,411) = HCF(8021,1522) = HCF(9543,8021) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8021, 9543 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 8021, 9543?

Answer: HCF of 8021, 9543 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8021, 9543 using Euclid's Algorithm?

Answer: For arbitrary numbers 8021, 9543 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.