Highest Common Factor of 863, 2338, 7310 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 863, 2338, 7310 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 863, 2338, 7310 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 863, 2338, 7310 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 863, 2338, 7310 is 1.

HCF(863, 2338, 7310) = 1

HCF of 863, 2338, 7310 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 863, 2338, 7310 is 1.

Highest Common Factor of 863,2338,7310 using Euclid's algorithm

Highest Common Factor of 863,2338,7310 is 1

Step 1: Since 2338 > 863, we apply the division lemma to 2338 and 863, to get

2338 = 863 x 2 + 612

Step 2: Since the reminder 863 ≠ 0, we apply division lemma to 612 and 863, to get

863 = 612 x 1 + 251

Step 3: We consider the new divisor 612 and the new remainder 251, and apply the division lemma to get

612 = 251 x 2 + 110

We consider the new divisor 251 and the new remainder 110,and apply the division lemma to get

251 = 110 x 2 + 31

We consider the new divisor 110 and the new remainder 31,and apply the division lemma to get

110 = 31 x 3 + 17

We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get

31 = 17 x 1 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 863 and 2338 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(110,31) = HCF(251,110) = HCF(612,251) = HCF(863,612) = HCF(2338,863) .

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

Step 1: Since 7310 > 1, we apply the division lemma to 7310 and 1, to get

7310 = 1 x 7310 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7310 is 1

Notice that 1 = HCF(7310,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 863, 2338, 7310 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 863, 2338, 7310?

Answer: HCF of 863, 2338, 7310 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 863, 2338, 7310 using Euclid's Algorithm?

Answer: For arbitrary numbers 863, 2338, 7310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.