Highest Common Factor of 6475, 7229 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 6475, 7229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6475, 7229 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 6475, 7229 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 6475, 7229 is 1.

HCF(6475, 7229) = 1

HCF of 6475, 7229 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 6475, 7229 is 1.

Highest Common Factor of 6475,7229 using Euclid's algorithm

Highest Common Factor of 6475,7229 is 1

Step 1: Since 7229 > 6475, we apply the division lemma to 7229 and 6475, to get

7229 = 6475 x 1 + 754

Step 2: Since the reminder 6475 ≠ 0, we apply division lemma to 754 and 6475, to get

6475 = 754 x 8 + 443

Step 3: We consider the new divisor 754 and the new remainder 443, and apply the division lemma to get

754 = 443 x 1 + 311

We consider the new divisor 443 and the new remainder 311,and apply the division lemma to get

443 = 311 x 1 + 132

We consider the new divisor 311 and the new remainder 132,and apply the division lemma to get

311 = 132 x 2 + 47

We consider the new divisor 132 and the new remainder 47,and apply the division lemma to get

132 = 47 x 2 + 38

We consider the new divisor 47 and the new remainder 38,and apply the division lemma to get

47 = 38 x 1 + 9

We consider the new divisor 38 and the new remainder 9,and apply the division lemma to get

38 = 9 x 4 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 6475 and 7229 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(38,9) = HCF(47,38) = HCF(132,47) = HCF(311,132) = HCF(443,311) = HCF(754,443) = HCF(6475,754) = HCF(7229,6475) .

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Frequently Asked Questions on HCF of 6475, 7229 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 6475, 7229?

Answer: HCF of 6475, 7229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6475, 7229 using Euclid's Algorithm?

Answer: For arbitrary numbers 6475, 7229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.