Highest Common Factor of 8375, 7130, 75063 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 8375, 7130, 75063 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8375, 7130, 75063 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 8375, 7130, 75063 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 8375, 7130, 75063 is 1.

HCF(8375, 7130, 75063) = 1

HCF of 8375, 7130, 75063 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 8375, 7130, 75063 is 1.

Highest Common Factor of 8375,7130,75063 using Euclid's algorithm

Highest Common Factor of 8375,7130,75063 is 1

Step 1: Since 8375 > 7130, we apply the division lemma to 8375 and 7130, to get

8375 = 7130 x 1 + 1245

Step 2: Since the reminder 7130 ≠ 0, we apply division lemma to 1245 and 7130, to get

7130 = 1245 x 5 + 905

Step 3: We consider the new divisor 1245 and the new remainder 905, and apply the division lemma to get

1245 = 905 x 1 + 340

We consider the new divisor 905 and the new remainder 340,and apply the division lemma to get

905 = 340 x 2 + 225

We consider the new divisor 340 and the new remainder 225,and apply the division lemma to get

340 = 225 x 1 + 115

We consider the new divisor 225 and the new remainder 115,and apply the division lemma to get

225 = 115 x 1 + 110

We consider the new divisor 115 and the new remainder 110,and apply the division lemma to get

115 = 110 x 1 + 5

We consider the new divisor 110 and the new remainder 5,and apply the division lemma to get

110 = 5 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 8375 and 7130 is 5

Notice that 5 = HCF(110,5) = HCF(115,110) = HCF(225,115) = HCF(340,225) = HCF(905,340) = HCF(1245,905) = HCF(7130,1245) = HCF(8375,7130) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 75063 > 5, we apply the division lemma to 75063 and 5, to get

75063 = 5 x 15012 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 75063 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(75063,5) .

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Frequently Asked Questions on HCF of 8375, 7130, 75063 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 8375, 7130, 75063?

Answer: HCF of 8375, 7130, 75063 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8375, 7130, 75063 using Euclid's Algorithm?

Answer: For arbitrary numbers 8375, 7130, 75063 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.