Highest Common Factor of 8301, 3002 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 8301, 3002 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8301, 3002 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 8301, 3002 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 8301, 3002 is 1.

HCF(8301, 3002) = 1

HCF of 8301, 3002 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 8301, 3002 is 1.

Highest Common Factor of 8301,3002 using Euclid's algorithm

Highest Common Factor of 8301,3002 is 1

Step 1: Since 8301 > 3002, we apply the division lemma to 8301 and 3002, to get

8301 = 3002 x 2 + 2297

Step 2: Since the reminder 3002 ≠ 0, we apply division lemma to 2297 and 3002, to get

3002 = 2297 x 1 + 705

Step 3: We consider the new divisor 2297 and the new remainder 705, and apply the division lemma to get

2297 = 705 x 3 + 182

We consider the new divisor 705 and the new remainder 182,and apply the division lemma to get

705 = 182 x 3 + 159

We consider the new divisor 182 and the new remainder 159,and apply the division lemma to get

182 = 159 x 1 + 23

We consider the new divisor 159 and the new remainder 23,and apply the division lemma to get

159 = 23 x 6 + 21

We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get

23 = 21 x 1 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 8301 and 3002 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(159,23) = HCF(182,159) = HCF(705,182) = HCF(2297,705) = HCF(3002,2297) = HCF(8301,3002) .

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Frequently Asked Questions on HCF of 8301, 3002 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 8301, 3002?

Answer: HCF of 8301, 3002 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8301, 3002 using Euclid's Algorithm?

Answer: For arbitrary numbers 8301, 3002 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.