Highest Common Factor of 7146, 5875 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 7146, 5875 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7146, 5875 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 7146, 5875 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 7146, 5875 is 1.

HCF(7146, 5875) = 1

HCF of 7146, 5875 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 7146, 5875 is 1.

Highest Common Factor of 7146,5875 using Euclid's algorithm

Highest Common Factor of 7146,5875 is 1

Step 1: Since 7146 > 5875, we apply the division lemma to 7146 and 5875, to get

7146 = 5875 x 1 + 1271

Step 2: Since the reminder 5875 ≠ 0, we apply division lemma to 1271 and 5875, to get

5875 = 1271 x 4 + 791

Step 3: We consider the new divisor 1271 and the new remainder 791, and apply the division lemma to get

1271 = 791 x 1 + 480

We consider the new divisor 791 and the new remainder 480,and apply the division lemma to get

791 = 480 x 1 + 311

We consider the new divisor 480 and the new remainder 311,and apply the division lemma to get

480 = 311 x 1 + 169

We consider the new divisor 311 and the new remainder 169,and apply the division lemma to get

311 = 169 x 1 + 142

We consider the new divisor 169 and the new remainder 142,and apply the division lemma to get

169 = 142 x 1 + 27

We consider the new divisor 142 and the new remainder 27,and apply the division lemma to get

142 = 27 x 5 + 7

We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get

27 = 7 x 3 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7146 and 5875 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(142,27) = HCF(169,142) = HCF(311,169) = HCF(480,311) = HCF(791,480) = HCF(1271,791) = HCF(5875,1271) = HCF(7146,5875) .

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Frequently Asked Questions on HCF of 7146, 5875 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 7146, 5875?

Answer: HCF of 7146, 5875 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7146, 5875 using Euclid's Algorithm?

Answer: For arbitrary numbers 7146, 5875 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.