Highest Common Factor of 605, 777, 103 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 605, 777, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 777, 103 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 605, 777, 103 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 605, 777, 103 is 1.

HCF(605, 777, 103) = 1

HCF of 605, 777, 103 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 605, 777, 103 is 1.

Highest Common Factor of 605,777,103 using Euclid's algorithm

Highest Common Factor of 605,777,103 is 1

Step 1: Since 777 > 605, we apply the division lemma to 777 and 605, to get

777 = 605 x 1 + 172

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 172 and 605, to get

605 = 172 x 3 + 89

Step 3: We consider the new divisor 172 and the new remainder 89, and apply the division lemma to get

172 = 89 x 1 + 83

We consider the new divisor 89 and the new remainder 83,and apply the division lemma to get

89 = 83 x 1 + 6

We consider the new divisor 83 and the new remainder 6,and apply the division lemma to get

83 = 6 x 13 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 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 605 and 777 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(83,6) = HCF(89,83) = HCF(172,89) = HCF(605,172) = HCF(777,605) .

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

Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get

103 = 1 x 103 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1

Notice that 1 = HCF(103,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 605, 777, 103 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 605, 777, 103?

Answer: HCF of 605, 777, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 777, 103 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 777, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.