Highest Common Factor of 660, 7195, 9302 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 660, 7195, 9302 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 7195, 9302 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 660, 7195, 9302 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 660, 7195, 9302 is 1.

HCF(660, 7195, 9302) = 1

HCF of 660, 7195, 9302 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 660, 7195, 9302 is 1.

Highest Common Factor of 660,7195,9302 using Euclid's algorithm

Highest Common Factor of 660,7195,9302 is 1

Step 1: Since 7195 > 660, we apply the division lemma to 7195 and 660, to get

7195 = 660 x 10 + 595

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 595 and 660, to get

660 = 595 x 1 + 65

Step 3: We consider the new divisor 595 and the new remainder 65, and apply the division lemma to get

595 = 65 x 9 + 10

We consider the new divisor 65 and the new remainder 10,and apply the division lemma to get

65 = 10 x 6 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 660 and 7195 is 5

Notice that 5 = HCF(10,5) = HCF(65,10) = HCF(595,65) = HCF(660,595) = HCF(7195,660) .

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

Step 1: Since 9302 > 5, we apply the division lemma to 9302 and 5, to get

9302 = 5 x 1860 + 2

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

5 = 2 x 2 + 1

Step 3: 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 9302 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(9302,5) .

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Frequently Asked Questions on HCF of 660, 7195, 9302 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 660, 7195, 9302?

Answer: HCF of 660, 7195, 9302 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 7195, 9302 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 7195, 9302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.