Highest Common Factor of 2177, 1991, 28695 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 2177, 1991, 28695 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2177, 1991, 28695 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 2177, 1991, 28695 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 2177, 1991, 28695 is 1.

HCF(2177, 1991, 28695) = 1

HCF of 2177, 1991, 28695 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 2177, 1991, 28695 is 1.

Highest Common Factor of 2177,1991,28695 using Euclid's algorithm

Highest Common Factor of 2177,1991,28695 is 1

Step 1: Since 2177 > 1991, we apply the division lemma to 2177 and 1991, to get

2177 = 1991 x 1 + 186

Step 2: Since the reminder 1991 ≠ 0, we apply division lemma to 186 and 1991, to get

1991 = 186 x 10 + 131

Step 3: We consider the new divisor 186 and the new remainder 131, and apply the division lemma to get

186 = 131 x 1 + 55

We consider the new divisor 131 and the new remainder 55,and apply the division lemma to get

131 = 55 x 2 + 21

We consider the new divisor 55 and the new remainder 21,and apply the division lemma to get

55 = 21 x 2 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2177 and 1991 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(55,21) = HCF(131,55) = HCF(186,131) = HCF(1991,186) = HCF(2177,1991) .

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

Step 1: Since 28695 > 1, we apply the division lemma to 28695 and 1, to get

28695 = 1 x 28695 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 28695 is 1

Notice that 1 = HCF(28695,1) .

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Frequently Asked Questions on HCF of 2177, 1991, 28695 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 2177, 1991, 28695?

Answer: HCF of 2177, 1991, 28695 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2177, 1991, 28695 using Euclid's Algorithm?

Answer: For arbitrary numbers 2177, 1991, 28695 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.