Highest Common Factor of 6801, 9008, 60912 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 6801, 9008, 60912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6801, 9008, 60912 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 6801, 9008, 60912 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 6801, 9008, 60912 is 1.

HCF(6801, 9008, 60912) = 1

HCF of 6801, 9008, 60912 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 6801, 9008, 60912 is 1.

Highest Common Factor of 6801,9008,60912 using Euclid's algorithm

Highest Common Factor of 6801,9008,60912 is 1

Step 1: Since 9008 > 6801, we apply the division lemma to 9008 and 6801, to get

9008 = 6801 x 1 + 2207

Step 2: Since the reminder 6801 ≠ 0, we apply division lemma to 2207 and 6801, to get

6801 = 2207 x 3 + 180

Step 3: We consider the new divisor 2207 and the new remainder 180, and apply the division lemma to get

2207 = 180 x 12 + 47

We consider the new divisor 180 and the new remainder 47,and apply the division lemma to get

180 = 47 x 3 + 39

We consider the new divisor 47 and the new remainder 39,and apply the division lemma to get

47 = 39 x 1 + 8

We consider the new divisor 39 and the new remainder 8,and apply the division lemma to get

39 = 8 x 4 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6801 and 9008 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(39,8) = HCF(47,39) = HCF(180,47) = HCF(2207,180) = HCF(6801,2207) = HCF(9008,6801) .

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

Step 1: Since 60912 > 1, we apply the division lemma to 60912 and 1, to get

60912 = 1 x 60912 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60912 is 1

Notice that 1 = HCF(60912,1) .

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Frequently Asked Questions on HCF of 6801, 9008, 60912 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 6801, 9008, 60912?

Answer: HCF of 6801, 9008, 60912 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6801, 9008, 60912 using Euclid's Algorithm?

Answer: For arbitrary numbers 6801, 9008, 60912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.