Highest Common Factor of 8166, 9906, 47620 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 8166, 9906, 47620 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8166, 9906, 47620 is 2 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 8166, 9906, 47620 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 8166, 9906, 47620 is 2.

HCF(8166, 9906, 47620) = 2

HCF of 8166, 9906, 47620 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 8166, 9906, 47620 is 2.

Highest Common Factor of 8166,9906,47620 using Euclid's algorithm

Highest Common Factor of 8166,9906,47620 is 2

Step 1: Since 9906 > 8166, we apply the division lemma to 9906 and 8166, to get

9906 = 8166 x 1 + 1740

Step 2: Since the reminder 8166 ≠ 0, we apply division lemma to 1740 and 8166, to get

8166 = 1740 x 4 + 1206

Step 3: We consider the new divisor 1740 and the new remainder 1206, and apply the division lemma to get

1740 = 1206 x 1 + 534

We consider the new divisor 1206 and the new remainder 534,and apply the division lemma to get

1206 = 534 x 2 + 138

We consider the new divisor 534 and the new remainder 138,and apply the division lemma to get

534 = 138 x 3 + 120

We consider the new divisor 138 and the new remainder 120,and apply the division lemma to get

138 = 120 x 1 + 18

We consider the new divisor 120 and the new remainder 18,and apply the division lemma to get

120 = 18 x 6 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 8166 and 9906 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(120,18) = HCF(138,120) = HCF(534,138) = HCF(1206,534) = HCF(1740,1206) = HCF(8166,1740) = HCF(9906,8166) .

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

Step 1: Since 47620 > 6, we apply the division lemma to 47620 and 6, to get

47620 = 6 x 7936 + 4

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get

6 = 4 x 1 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 47620 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(47620,6) .

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Frequently Asked Questions on HCF of 8166, 9906, 47620 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 8166, 9906, 47620?

Answer: HCF of 8166, 9906, 47620 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8166, 9906, 47620 using Euclid's Algorithm?

Answer: For arbitrary numbers 8166, 9906, 47620 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.