Highest Common Factor of 2194, 8201, 78869 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 2194, 8201, 78869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2194, 8201, 78869 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 2194, 8201, 78869 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 2194, 8201, 78869 is 1.

HCF(2194, 8201, 78869) = 1

HCF of 2194, 8201, 78869 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 2194, 8201, 78869 is 1.

Highest Common Factor of 2194,8201,78869 using Euclid's algorithm

Highest Common Factor of 2194,8201,78869 is 1

Step 1: Since 8201 > 2194, we apply the division lemma to 8201 and 2194, to get

8201 = 2194 x 3 + 1619

Step 2: Since the reminder 2194 ≠ 0, we apply division lemma to 1619 and 2194, to get

2194 = 1619 x 1 + 575

Step 3: We consider the new divisor 1619 and the new remainder 575, and apply the division lemma to get

1619 = 575 x 2 + 469

We consider the new divisor 575 and the new remainder 469,and apply the division lemma to get

575 = 469 x 1 + 106

We consider the new divisor 469 and the new remainder 106,and apply the division lemma to get

469 = 106 x 4 + 45

We consider the new divisor 106 and the new remainder 45,and apply the division lemma to get

106 = 45 x 2 + 16

We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get

45 = 16 x 2 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2194 and 8201 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(106,45) = HCF(469,106) = HCF(575,469) = HCF(1619,575) = HCF(2194,1619) = HCF(8201,2194) .

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

Step 1: Since 78869 > 1, we apply the division lemma to 78869 and 1, to get

78869 = 1 x 78869 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78869 is 1

Notice that 1 = HCF(78869,1) .

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Frequently Asked Questions on HCF of 2194, 8201, 78869 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 2194, 8201, 78869?

Answer: HCF of 2194, 8201, 78869 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2194, 8201, 78869 using Euclid's Algorithm?

Answer: For arbitrary numbers 2194, 8201, 78869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.