Highest Common Factor of 716, 913, 266 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 716, 913, 266 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 716, 913, 266 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 716, 913, 266 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 716, 913, 266 is 1.

HCF(716, 913, 266) = 1

HCF of 716, 913, 266 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 716, 913, 266 is 1.

Highest Common Factor of 716,913,266 using Euclid's algorithm

Highest Common Factor of 716,913,266 is 1

Step 1: Since 913 > 716, we apply the division lemma to 913 and 716, to get

913 = 716 x 1 + 197

Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 197 and 716, to get

716 = 197 x 3 + 125

Step 3: We consider the new divisor 197 and the new remainder 125, and apply the division lemma to get

197 = 125 x 1 + 72

We consider the new divisor 125 and the new remainder 72,and apply the division lemma to get

125 = 72 x 1 + 53

We consider the new divisor 72 and the new remainder 53,and apply the division lemma to get

72 = 53 x 1 + 19

We consider the new divisor 53 and the new remainder 19,and apply the division lemma to get

53 = 19 x 2 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 716 and 913 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(53,19) = HCF(72,53) = HCF(125,72) = HCF(197,125) = HCF(716,197) = HCF(913,716) .

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

Step 1: Since 266 > 1, we apply the division lemma to 266 and 1, to get

266 = 1 x 266 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 266 is 1

Notice that 1 = HCF(266,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 716, 913, 266 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 716, 913, 266?

Answer: HCF of 716, 913, 266 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 716, 913, 266 using Euclid's Algorithm?

Answer: For arbitrary numbers 716, 913, 266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.