Highest Common Factor of 2728, 1813, 31777 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 2728, 1813, 31777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2728, 1813, 31777 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 2728, 1813, 31777 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 2728, 1813, 31777 is 1.

HCF(2728, 1813, 31777) = 1

HCF of 2728, 1813, 31777 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 2728, 1813, 31777 is 1.

Highest Common Factor of 2728,1813,31777 using Euclid's algorithm

Highest Common Factor of 2728,1813,31777 is 1

Step 1: Since 2728 > 1813, we apply the division lemma to 2728 and 1813, to get

2728 = 1813 x 1 + 915

Step 2: Since the reminder 1813 ≠ 0, we apply division lemma to 915 and 1813, to get

1813 = 915 x 1 + 898

Step 3: We consider the new divisor 915 and the new remainder 898, and apply the division lemma to get

915 = 898 x 1 + 17

We consider the new divisor 898 and the new remainder 17,and apply the division lemma to get

898 = 17 x 52 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 2728 and 1813 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(898,17) = HCF(915,898) = HCF(1813,915) = HCF(2728,1813) .

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

Step 1: Since 31777 > 1, we apply the division lemma to 31777 and 1, to get

31777 = 1 x 31777 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31777 is 1

Notice that 1 = HCF(31777,1) .

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Frequently Asked Questions on HCF of 2728, 1813, 31777 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 2728, 1813, 31777?

Answer: HCF of 2728, 1813, 31777 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2728, 1813, 31777 using Euclid's Algorithm?

Answer: For arbitrary numbers 2728, 1813, 31777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.