Highest Common Factor of 431, 7593, 6975 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 431, 7593, 6975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 431, 7593, 6975 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 431, 7593, 6975 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 431, 7593, 6975 is 1.

HCF(431, 7593, 6975) = 1

HCF of 431, 7593, 6975 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 431, 7593, 6975 is 1.

Highest Common Factor of 431,7593,6975 using Euclid's algorithm

Highest Common Factor of 431,7593,6975 is 1

Step 1: Since 7593 > 431, we apply the division lemma to 7593 and 431, to get

7593 = 431 x 17 + 266

Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 266 and 431, to get

431 = 266 x 1 + 165

Step 3: We consider the new divisor 266 and the new remainder 165, and apply the division lemma to get

266 = 165 x 1 + 101

We consider the new divisor 165 and the new remainder 101,and apply the division lemma to get

165 = 101 x 1 + 64

We consider the new divisor 101 and the new remainder 64,and apply the division lemma to get

101 = 64 x 1 + 37

We consider the new divisor 64 and the new remainder 37,and apply the division lemma to get

64 = 37 x 1 + 27

We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get

37 = 27 x 1 + 10

We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get

27 = 10 x 2 + 7

We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get

10 = 7 x 1 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 431 and 7593 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(64,37) = HCF(101,64) = HCF(165,101) = HCF(266,165) = HCF(431,266) = HCF(7593,431) .

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

Step 1: Since 6975 > 1, we apply the division lemma to 6975 and 1, to get

6975 = 1 x 6975 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6975 is 1

Notice that 1 = HCF(6975,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 431, 7593, 6975 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 431, 7593, 6975?

Answer: HCF of 431, 7593, 6975 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 431, 7593, 6975 using Euclid's Algorithm?

Answer: For arbitrary numbers 431, 7593, 6975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.