Highest Common Factor of 777, 716, 145 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, 716, 145 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 777, 716, 145 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, 716, 145 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, 716, 145 is 1.

HCF(777, 716, 145) = 1

HCF of 777, 716, 145 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, 716, 145 is 1.

Highest Common Factor of 777,716,145 using Euclid's algorithm

Highest Common Factor of 777,716,145 is 1

Step 1: Since 777 > 716, we apply the division lemma to 777 and 716, to get

777 = 716 x 1 + 61

Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 61 and 716, to get

716 = 61 x 11 + 45

Step 3: We consider the new divisor 61 and the new remainder 45, and apply the division lemma to get

61 = 45 x 1 + 16

We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get

45 = 16 x 2 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 777 and 716 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(61,45) = HCF(716,61) = HCF(777,716) .

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

Step 1: Since 145 > 1, we apply the division lemma to 145 and 1, to get

145 = 1 x 145 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 145 is 1

Notice that 1 = HCF(145,1) .

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, 716, 145 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, 716, 145?

Answer: HCF of 777, 716, 145 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 777, 716, 145 using Euclid's Algorithm?

Answer: For arbitrary numbers 777, 716, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.