Highest Common Factor of 6886, 8104, 65664 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 6886, 8104, 65664 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6886, 8104, 65664 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 6886, 8104, 65664 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 6886, 8104, 65664 is 2.

HCF(6886, 8104, 65664) = 2

HCF of 6886, 8104, 65664 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 6886, 8104, 65664 is 2.

Highest Common Factor of 6886,8104,65664 using Euclid's algorithm

Highest Common Factor of 6886,8104,65664 is 2

Step 1: Since 8104 > 6886, we apply the division lemma to 8104 and 6886, to get

8104 = 6886 x 1 + 1218

Step 2: Since the reminder 6886 ≠ 0, we apply division lemma to 1218 and 6886, to get

6886 = 1218 x 5 + 796

Step 3: We consider the new divisor 1218 and the new remainder 796, and apply the division lemma to get

1218 = 796 x 1 + 422

We consider the new divisor 796 and the new remainder 422,and apply the division lemma to get

796 = 422 x 1 + 374

We consider the new divisor 422 and the new remainder 374,and apply the division lemma to get

422 = 374 x 1 + 48

We consider the new divisor 374 and the new remainder 48,and apply the division lemma to get

374 = 48 x 7 + 38

We consider the new divisor 48 and the new remainder 38,and apply the division lemma to get

48 = 38 x 1 + 10

We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get

38 = 10 x 3 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6886 and 8104 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(48,38) = HCF(374,48) = HCF(422,374) = HCF(796,422) = HCF(1218,796) = HCF(6886,1218) = HCF(8104,6886) .

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

Step 1: Since 65664 > 2, we apply the division lemma to 65664 and 2, to get

65664 = 2 x 32832 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 65664 is 2

Notice that 2 = HCF(65664,2) .

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Frequently Asked Questions on HCF of 6886, 8104, 65664 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 6886, 8104, 65664?

Answer: HCF of 6886, 8104, 65664 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6886, 8104, 65664 using Euclid's Algorithm?

Answer: For arbitrary numbers 6886, 8104, 65664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.