Highest Common Factor of 8175, 728 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 8175, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8175, 728 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 8175, 728 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 8175, 728 is 1.

HCF(8175, 728) = 1

HCF of 8175, 728 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 8175, 728 is 1.

Highest Common Factor of 8175,728 using Euclid's algorithm

Highest Common Factor of 8175,728 is 1

Step 1: Since 8175 > 728, we apply the division lemma to 8175 and 728, to get

8175 = 728 x 11 + 167

Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 167 and 728, to get

728 = 167 x 4 + 60

Step 3: We consider the new divisor 167 and the new remainder 60, and apply the division lemma to get

167 = 60 x 2 + 47

We consider the new divisor 60 and the new remainder 47,and apply the division lemma to get

60 = 47 x 1 + 13

We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get

47 = 13 x 3 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 8175 and 728 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(60,47) = HCF(167,60) = HCF(728,167) = HCF(8175,728) .

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Frequently Asked Questions on HCF of 8175, 728 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 8175, 728?

Answer: HCF of 8175, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8175, 728 using Euclid's Algorithm?

Answer: For arbitrary numbers 8175, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.