Highest Common Factor of 663, 386, 854 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 663, 386, 854 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 386, 854 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 663, 386, 854 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 663, 386, 854 is 1.

HCF(663, 386, 854) = 1

HCF of 663, 386, 854 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 663, 386, 854 is 1.

Highest Common Factor of 663,386,854 using Euclid's algorithm

Highest Common Factor of 663,386,854 is 1

Step 1: Since 663 > 386, we apply the division lemma to 663 and 386, to get

663 = 386 x 1 + 277

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 277 and 386, to get

386 = 277 x 1 + 109

Step 3: We consider the new divisor 277 and the new remainder 109, and apply the division lemma to get

277 = 109 x 2 + 59

We consider the new divisor 109 and the new remainder 59,and apply the division lemma to get

109 = 59 x 1 + 50

We consider the new divisor 59 and the new remainder 50,and apply the division lemma to get

59 = 50 x 1 + 9

We consider the new divisor 50 and the new remainder 9,and apply the division lemma to get

50 = 9 x 5 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 663 and 386 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(50,9) = HCF(59,50) = HCF(109,59) = HCF(277,109) = HCF(386,277) = HCF(663,386) .

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

Step 1: Since 854 > 1, we apply the division lemma to 854 and 1, to get

854 = 1 x 854 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 854 is 1

Notice that 1 = HCF(854,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 663, 386, 854 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 663, 386, 854?

Answer: HCF of 663, 386, 854 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 386, 854 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 386, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.