Highest Common Factor of 8121, 9985, 62006 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 8121, 9985, 62006 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8121, 9985, 62006 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 8121, 9985, 62006 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 8121, 9985, 62006 is 1.

HCF(8121, 9985, 62006) = 1

HCF of 8121, 9985, 62006 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 8121, 9985, 62006 is 1.

Highest Common Factor of 8121,9985,62006 using Euclid's algorithm

Highest Common Factor of 8121,9985,62006 is 1

Step 1: Since 9985 > 8121, we apply the division lemma to 9985 and 8121, to get

9985 = 8121 x 1 + 1864

Step 2: Since the reminder 8121 ≠ 0, we apply division lemma to 1864 and 8121, to get

8121 = 1864 x 4 + 665

Step 3: We consider the new divisor 1864 and the new remainder 665, and apply the division lemma to get

1864 = 665 x 2 + 534

We consider the new divisor 665 and the new remainder 534,and apply the division lemma to get

665 = 534 x 1 + 131

We consider the new divisor 534 and the new remainder 131,and apply the division lemma to get

534 = 131 x 4 + 10

We consider the new divisor 131 and the new remainder 10,and apply the division lemma to get

131 = 10 x 13 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8121 and 9985 is 1

Notice that 1 = HCF(10,1) = HCF(131,10) = HCF(534,131) = HCF(665,534) = HCF(1864,665) = HCF(8121,1864) = HCF(9985,8121) .

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

Step 1: Since 62006 > 1, we apply the division lemma to 62006 and 1, to get

62006 = 1 x 62006 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 62006 is 1

Notice that 1 = HCF(62006,1) .

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Frequently Asked Questions on HCF of 8121, 9985, 62006 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 8121, 9985, 62006?

Answer: HCF of 8121, 9985, 62006 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8121, 9985, 62006 using Euclid's Algorithm?

Answer: For arbitrary numbers 8121, 9985, 62006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.