Highest Common Factor of 5005, 7101 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 5005, 7101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5005, 7101 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 5005, 7101 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 5005, 7101 is 1.

HCF(5005, 7101) = 1

HCF of 5005, 7101 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 5005, 7101 is 1.

Highest Common Factor of 5005,7101 using Euclid's algorithm

Highest Common Factor of 5005,7101 is 1

Step 1: Since 7101 > 5005, we apply the division lemma to 7101 and 5005, to get

7101 = 5005 x 1 + 2096

Step 2: Since the reminder 5005 ≠ 0, we apply division lemma to 2096 and 5005, to get

5005 = 2096 x 2 + 813

Step 3: We consider the new divisor 2096 and the new remainder 813, and apply the division lemma to get

2096 = 813 x 2 + 470

We consider the new divisor 813 and the new remainder 470,and apply the division lemma to get

813 = 470 x 1 + 343

We consider the new divisor 470 and the new remainder 343,and apply the division lemma to get

470 = 343 x 1 + 127

We consider the new divisor 343 and the new remainder 127,and apply the division lemma to get

343 = 127 x 2 + 89

We consider the new divisor 127 and the new remainder 89,and apply the division lemma to get

127 = 89 x 1 + 38

We consider the new divisor 89 and the new remainder 38,and apply the division lemma to get

89 = 38 x 2 + 13

We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get

38 = 13 x 2 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5005 and 7101 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(89,38) = HCF(127,89) = HCF(343,127) = HCF(470,343) = HCF(813,470) = HCF(2096,813) = HCF(5005,2096) = HCF(7101,5005) .

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Frequently Asked Questions on HCF of 5005, 7101 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 5005, 7101?

Answer: HCF of 5005, 7101 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5005, 7101 using Euclid's Algorithm?

Answer: For arbitrary numbers 5005, 7101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.