Highest Common Factor of 6005, 9605, 70068 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 6005, 9605, 70068 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6005, 9605, 70068 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 6005, 9605, 70068 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 6005, 9605, 70068 is 1.

HCF(6005, 9605, 70068) = 1

HCF of 6005, 9605, 70068 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 6005, 9605, 70068 is 1.

Highest Common Factor of 6005,9605,70068 using Euclid's algorithm

Highest Common Factor of 6005,9605,70068 is 1

Step 1: Since 9605 > 6005, we apply the division lemma to 9605 and 6005, to get

9605 = 6005 x 1 + 3600

Step 2: Since the reminder 6005 ≠ 0, we apply division lemma to 3600 and 6005, to get

6005 = 3600 x 1 + 2405

Step 3: We consider the new divisor 3600 and the new remainder 2405, and apply the division lemma to get

3600 = 2405 x 1 + 1195

We consider the new divisor 2405 and the new remainder 1195,and apply the division lemma to get

2405 = 1195 x 2 + 15

We consider the new divisor 1195 and the new remainder 15,and apply the division lemma to get

1195 = 15 x 79 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 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 6005 and 9605 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(1195,15) = HCF(2405,1195) = HCF(3600,2405) = HCF(6005,3600) = HCF(9605,6005) .

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

Step 1: Since 70068 > 5, we apply the division lemma to 70068 and 5, to get

70068 = 5 x 14013 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 5 and 70068 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(70068,5) .

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Frequently Asked Questions on HCF of 6005, 9605, 70068 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 6005, 9605, 70068?

Answer: HCF of 6005, 9605, 70068 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6005, 9605, 70068 using Euclid's Algorithm?

Answer: For arbitrary numbers 6005, 9605, 70068 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.