Highest Common Factor of 6545, 1165 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 6545, 1165 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 6545, 1165 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 6545, 1165 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 6545, 1165 is 5.

HCF(6545, 1165) = 5

HCF of 6545, 1165 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 6545, 1165 is 5.

Highest Common Factor of 6545,1165 using Euclid's algorithm

Highest Common Factor of 6545,1165 is 5

Step 1: Since 6545 > 1165, we apply the division lemma to 6545 and 1165, to get

6545 = 1165 x 5 + 720

Step 2: Since the reminder 1165 ≠ 0, we apply division lemma to 720 and 1165, to get

1165 = 720 x 1 + 445

Step 3: We consider the new divisor 720 and the new remainder 445, and apply the division lemma to get

720 = 445 x 1 + 275

We consider the new divisor 445 and the new remainder 275,and apply the division lemma to get

445 = 275 x 1 + 170

We consider the new divisor 275 and the new remainder 170,and apply the division lemma to get

275 = 170 x 1 + 105

We consider the new divisor 170 and the new remainder 105,and apply the division lemma to get

170 = 105 x 1 + 65

We consider the new divisor 105 and the new remainder 65,and apply the division lemma to get

105 = 65 x 1 + 40

We consider the new divisor 65 and the new remainder 40,and apply the division lemma to get

65 = 40 x 1 + 25

We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get

40 = 25 x 1 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6545 and 1165 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(65,40) = HCF(105,65) = HCF(170,105) = HCF(275,170) = HCF(445,275) = HCF(720,445) = HCF(1165,720) = HCF(6545,1165) .

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Frequently Asked Questions on HCF of 6545, 1165 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 6545, 1165?

Answer: HCF of 6545, 1165 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6545, 1165 using Euclid's Algorithm?

Answer: For arbitrary numbers 6545, 1165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.