Highest Common Factor of 8069, 7003, 21646 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 8069, 7003, 21646 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8069, 7003, 21646 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 8069, 7003, 21646 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 8069, 7003, 21646 is 1.

HCF(8069, 7003, 21646) = 1

HCF of 8069, 7003, 21646 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 8069, 7003, 21646 is 1.

Highest Common Factor of 8069,7003,21646 using Euclid's algorithm

Highest Common Factor of 8069,7003,21646 is 1

Step 1: Since 8069 > 7003, we apply the division lemma to 8069 and 7003, to get

8069 = 7003 x 1 + 1066

Step 2: Since the reminder 7003 ≠ 0, we apply division lemma to 1066 and 7003, to get

7003 = 1066 x 6 + 607

Step 3: We consider the new divisor 1066 and the new remainder 607, and apply the division lemma to get

1066 = 607 x 1 + 459

We consider the new divisor 607 and the new remainder 459,and apply the division lemma to get

607 = 459 x 1 + 148

We consider the new divisor 459 and the new remainder 148,and apply the division lemma to get

459 = 148 x 3 + 15

We consider the new divisor 148 and the new remainder 15,and apply the division lemma to get

148 = 15 x 9 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 8069 and 7003 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(148,15) = HCF(459,148) = HCF(607,459) = HCF(1066,607) = HCF(7003,1066) = HCF(8069,7003) .

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

Step 1: Since 21646 > 1, we apply the division lemma to 21646 and 1, to get

21646 = 1 x 21646 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21646 is 1

Notice that 1 = HCF(21646,1) .

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Frequently Asked Questions on HCF of 8069, 7003, 21646 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 8069, 7003, 21646?

Answer: HCF of 8069, 7003, 21646 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8069, 7003, 21646 using Euclid's Algorithm?

Answer: For arbitrary numbers 8069, 7003, 21646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.