Highest Common Factor of 827, 720, 863 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 827, 720, 863 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 720, 863 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 827, 720, 863 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 827, 720, 863 is 1.

HCF(827, 720, 863) = 1

HCF of 827, 720, 863 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 827, 720, 863 is 1.

Highest Common Factor of 827,720,863 using Euclid's algorithm

Highest Common Factor of 827,720,863 is 1

Step 1: Since 827 > 720, we apply the division lemma to 827 and 720, to get

827 = 720 x 1 + 107

Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 107 and 720, to get

720 = 107 x 6 + 78

Step 3: We consider the new divisor 107 and the new remainder 78, and apply the division lemma to get

107 = 78 x 1 + 29

We consider the new divisor 78 and the new remainder 29,and apply the division lemma to get

78 = 29 x 2 + 20

We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get

29 = 20 x 1 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 827 and 720 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(78,29) = HCF(107,78) = HCF(720,107) = HCF(827,720) .


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

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

863 = 1 x 863 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 863 is 1

Notice that 1 = HCF(863,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 827, 720, 863 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 827, 720, 863?

Answer: HCF of 827, 720, 863 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 720, 863 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 720, 863 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.