Highest Common Factor of 5105, 8065 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 5105, 8065 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 5105, 8065 is 5 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 5105, 8065 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 5105, 8065 is 5.

HCF(5105, 8065) = 5

HCF of 5105, 8065 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 5105, 8065 is 5.

Highest Common Factor of 5105,8065 using Euclid's algorithm

Highest Common Factor of 5105,8065 is 5

Step 1: Since 8065 > 5105, we apply the division lemma to 8065 and 5105, to get

8065 = 5105 x 1 + 2960

Step 2: Since the reminder 5105 ≠ 0, we apply division lemma to 2960 and 5105, to get

5105 = 2960 x 1 + 2145

Step 3: We consider the new divisor 2960 and the new remainder 2145, and apply the division lemma to get

2960 = 2145 x 1 + 815

We consider the new divisor 2145 and the new remainder 815,and apply the division lemma to get

2145 = 815 x 2 + 515

We consider the new divisor 815 and the new remainder 515,and apply the division lemma to get

815 = 515 x 1 + 300

We consider the new divisor 515 and the new remainder 300,and apply the division lemma to get

515 = 300 x 1 + 215

We consider the new divisor 300 and the new remainder 215,and apply the division lemma to get

300 = 215 x 1 + 85

We consider the new divisor 215 and the new remainder 85,and apply the division lemma to get

215 = 85 x 2 + 45

We consider the new divisor 85 and the new remainder 45,and apply the division lemma to get

85 = 45 x 1 + 40

We consider the new divisor 45 and the new remainder 40,and apply the division lemma to get

45 = 40 x 1 + 5

We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get

40 = 5 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5105 and 8065 is 5

Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(85,45) = HCF(215,85) = HCF(300,215) = HCF(515,300) = HCF(815,515) = HCF(2145,815) = HCF(2960,2145) = HCF(5105,2960) = HCF(8065,5105) .

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Frequently Asked Questions on HCF of 5105, 8065 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 5105, 8065?

Answer: HCF of 5105, 8065 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5105, 8065 using Euclid's Algorithm?

Answer: For arbitrary numbers 5105, 8065 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.