Highest Common Factor of 854, 673, 305 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 854, 673, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 673, 305 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 854, 673, 305 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 854, 673, 305 is 1.

HCF(854, 673, 305) = 1

HCF of 854, 673, 305 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 854, 673, 305 is 1.

Highest Common Factor of 854,673,305 using Euclid's algorithm

Highest Common Factor of 854,673,305 is 1

Step 1: Since 854 > 673, we apply the division lemma to 854 and 673, to get

854 = 673 x 1 + 181

Step 2: Since the reminder 673 ≠ 0, we apply division lemma to 181 and 673, to get

673 = 181 x 3 + 130

Step 3: We consider the new divisor 181 and the new remainder 130, and apply the division lemma to get

181 = 130 x 1 + 51

We consider the new divisor 130 and the new remainder 51,and apply the division lemma to get

130 = 51 x 2 + 28

We consider the new divisor 51 and the new remainder 28,and apply the division lemma to get

51 = 28 x 1 + 23

We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get

28 = 23 x 1 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

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

5 = 3 x 1 + 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 854 and 673 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(51,28) = HCF(130,51) = HCF(181,130) = HCF(673,181) = HCF(854,673) .

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

Step 1: Since 305 > 1, we apply the division lemma to 305 and 1, to get

305 = 1 x 305 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 305 is 1

Notice that 1 = HCF(305,1) .

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Frequently Asked Questions on HCF of 854, 673, 305 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 854, 673, 305?

Answer: HCF of 854, 673, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 673, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 673, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.