Highest Common Factor of 80, 866, 318 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 80, 866, 318 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 80, 866, 318 is 2 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 80, 866, 318 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 80, 866, 318 is 2.

HCF(80, 866, 318) = 2

HCF of 80, 866, 318 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 80, 866, 318 is 2.

Highest Common Factor of 80,866,318 using Euclid's algorithm

Highest Common Factor of 80,866,318 is 2

Step 1: Since 866 > 80, we apply the division lemma to 866 and 80, to get

866 = 80 x 10 + 66

Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 66 and 80, to get

80 = 66 x 1 + 14

Step 3: We consider the new divisor 66 and the new remainder 14, and apply the division lemma to get

66 = 14 x 4 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 80 and 866 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(80,66) = HCF(866,80) .

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

Step 1: Since 318 > 2, we apply the division lemma to 318 and 2, to get

318 = 2 x 159 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 318 is 2

Notice that 2 = HCF(318,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 80, 866, 318 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 80, 866, 318?

Answer: HCF of 80, 866, 318 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 80, 866, 318 using Euclid's Algorithm?

Answer: For arbitrary numbers 80, 866, 318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.