Highest Common Factor of 180, 768, 823 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 180, 768, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 768, 823 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 180, 768, 823 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 180, 768, 823 is 1.

HCF(180, 768, 823) = 1

HCF of 180, 768, 823 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 180, 768, 823 is 1.

Highest Common Factor of 180,768,823 using Euclid's algorithm

Highest Common Factor of 180,768,823 is 1

Step 1: Since 768 > 180, we apply the division lemma to 768 and 180, to get

768 = 180 x 4 + 48

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 48 and 180, to get

180 = 48 x 3 + 36

Step 3: We consider the new divisor 48 and the new remainder 36, and apply the division lemma to get

48 = 36 x 1 + 12

We consider the new divisor 36 and the new remainder 12, and apply the division lemma to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 180 and 768 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(180,48) = HCF(768,180) .

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

Step 1: Since 823 > 12, we apply the division lemma to 823 and 12, to get

823 = 12 x 68 + 7

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 7 and 12, to get

12 = 7 x 1 + 5

Step 3: We consider the new divisor 7 and the new remainder 5, and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 12 and 823 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(823,12) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 180, 768, 823 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 180, 768, 823?

Answer: HCF of 180, 768, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 768, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 768, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.