Highest Common Factor of 6475, 3768 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, 3768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6475, 3768 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, 3768 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, 3768 is 1.

HCF(6475, 3768) = 1

HCF of 6475, 3768 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, 3768 is 1.

Highest Common Factor of 6475,3768 using Euclid's algorithm

Highest Common Factor of 6475,3768 is 1

Step 1: Since 6475 > 3768, we apply the division lemma to 6475 and 3768, to get

6475 = 3768 x 1 + 2707

Step 2: Since the reminder 3768 ≠ 0, we apply division lemma to 2707 and 3768, to get

3768 = 2707 x 1 + 1061

Step 3: We consider the new divisor 2707 and the new remainder 1061, and apply the division lemma to get

2707 = 1061 x 2 + 585

We consider the new divisor 1061 and the new remainder 585,and apply the division lemma to get

1061 = 585 x 1 + 476

We consider the new divisor 585 and the new remainder 476,and apply the division lemma to get

585 = 476 x 1 + 109

We consider the new divisor 476 and the new remainder 109,and apply the division lemma to get

476 = 109 x 4 + 40

We consider the new divisor 109 and the new remainder 40,and apply the division lemma to get

109 = 40 x 2 + 29

We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get

40 = 29 x 1 + 11

We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get

29 = 11 x 2 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6475 and 3768 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(109,40) = HCF(476,109) = HCF(585,476) = HCF(1061,585) = HCF(2707,1061) = HCF(3768,2707) = HCF(6475,3768) .

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Frequently Asked Questions on HCF of 6475, 3768 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, 3768?

Answer: HCF of 6475, 3768 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6475, 3768 using Euclid's Algorithm?

Answer: For arbitrary numbers 6475, 3768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.