Highest Common Factor of 777, 475, 65 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 777, 475, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 777, 475, 65 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 777, 475, 65 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 777, 475, 65 is 1.

HCF(777, 475, 65) = 1

HCF of 777, 475, 65 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 777, 475, 65 is 1.

Highest Common Factor of 777,475,65 using Euclid's algorithm

Highest Common Factor of 777,475,65 is 1

Step 1: Since 777 > 475, we apply the division lemma to 777 and 475, to get

777 = 475 x 1 + 302

Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 302 and 475, to get

475 = 302 x 1 + 173

Step 3: We consider the new divisor 302 and the new remainder 173, and apply the division lemma to get

302 = 173 x 1 + 129

We consider the new divisor 173 and the new remainder 129,and apply the division lemma to get

173 = 129 x 1 + 44

We consider the new divisor 129 and the new remainder 44,and apply the division lemma to get

129 = 44 x 2 + 41

We consider the new divisor 44 and the new remainder 41,and apply the division lemma to get

44 = 41 x 1 + 3

We consider the new divisor 41 and the new remainder 3,and apply the division lemma to get

41 = 3 x 13 + 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 777 and 475 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(129,44) = HCF(173,129) = HCF(302,173) = HCF(475,302) = HCF(777,475) .

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

Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get

65 = 1 x 65 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1

Notice that 1 = HCF(65,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 777, 475, 65 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 777, 475, 65?

Answer: HCF of 777, 475, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 777, 475, 65 using Euclid's Algorithm?

Answer: For arbitrary numbers 777, 475, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.