Highest Common Factor of 997, 612, 129 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, 612, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 997, 612, 129 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, 612, 129 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, 612, 129 is 1.

HCF(997, 612, 129) = 1

HCF of 997, 612, 129 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, 612, 129 is 1.

Highest Common Factor of 997,612,129 using Euclid's algorithm

Highest Common Factor of 997,612,129 is 1

Step 1: Since 997 > 612, we apply the division lemma to 997 and 612, to get

997 = 612 x 1 + 385

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 385 and 612, to get

612 = 385 x 1 + 227

Step 3: We consider the new divisor 385 and the new remainder 227, and apply the division lemma to get

385 = 227 x 1 + 158

We consider the new divisor 227 and the new remainder 158,and apply the division lemma to get

227 = 158 x 1 + 69

We consider the new divisor 158 and the new remainder 69,and apply the division lemma to get

158 = 69 x 2 + 20

We consider the new divisor 69 and the new remainder 20,and apply the division lemma to get

69 = 20 x 3 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 997 and 612 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(69,20) = HCF(158,69) = HCF(227,158) = HCF(385,227) = HCF(612,385) = HCF(997,612) .

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

Step 1: Since 129 > 1, we apply the division lemma to 129 and 1, to get

129 = 1 x 129 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 129 is 1

Notice that 1 = HCF(129,1) .

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, 612, 129 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, 612, 129?

Answer: HCF of 997, 612, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 997, 612, 129 using Euclid's Algorithm?

Answer: For arbitrary numbers 997, 612, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.