Highest Common Factor of 997, 2780 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 997, 2780 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 997, 2780 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 997, 2780 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 997, 2780 is 1.

HCF(997, 2780) = 1

HCF of 997, 2780 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 997, 2780 is 1.

Highest Common Factor of 997,2780 using Euclid's algorithm

Highest Common Factor of 997,2780 is 1

Step 1: Since 2780 > 997, we apply the division lemma to 2780 and 997, to get

2780 = 997 x 2 + 786

Step 2: Since the reminder 997 ≠ 0, we apply division lemma to 786 and 997, to get

997 = 786 x 1 + 211

Step 3: We consider the new divisor 786 and the new remainder 211, and apply the division lemma to get

786 = 211 x 3 + 153

We consider the new divisor 211 and the new remainder 153,and apply the division lemma to get

211 = 153 x 1 + 58

We consider the new divisor 153 and the new remainder 58,and apply the division lemma to get

153 = 58 x 2 + 37

We consider the new divisor 58 and the new remainder 37,and apply the division lemma to get

58 = 37 x 1 + 21

We consider the new divisor 37 and the new remainder 21,and apply the division lemma to get

37 = 21 x 1 + 16

We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get

21 = 16 x 1 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 997 and 2780 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(37,21) = HCF(58,37) = HCF(153,58) = HCF(211,153) = HCF(786,211) = HCF(997,786) = HCF(2780,997) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 997, 2780 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 997, 2780?

Answer: HCF of 997, 2780 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 997, 2780 using Euclid's Algorithm?

Answer: For arbitrary numbers 997, 2780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.