Highest Common Factor of 673, 389, 257 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 673, 389, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 389, 257 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 673, 389, 257 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 673, 389, 257 is 1.

HCF(673, 389, 257) = 1

HCF of 673, 389, 257 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 673, 389, 257 is 1.

Highest Common Factor of 673,389,257 using Euclid's algorithm

Highest Common Factor of 673,389,257 is 1

Step 1: Since 673 > 389, we apply the division lemma to 673 and 389, to get

673 = 389 x 1 + 284

Step 2: Since the reminder 389 ≠ 0, we apply division lemma to 284 and 389, to get

389 = 284 x 1 + 105

Step 3: We consider the new divisor 284 and the new remainder 105, and apply the division lemma to get

284 = 105 x 2 + 74

We consider the new divisor 105 and the new remainder 74,and apply the division lemma to get

105 = 74 x 1 + 31

We consider the new divisor 74 and the new remainder 31,and apply the division lemma to get

74 = 31 x 2 + 12

We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

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 673 and 389 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(74,31) = HCF(105,74) = HCF(284,105) = HCF(389,284) = HCF(673,389) .

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

Step 1: Since 257 > 1, we apply the division lemma to 257 and 1, to get

257 = 1 x 257 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 257 is 1

Notice that 1 = HCF(257,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 673, 389, 257 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 673, 389, 257?

Answer: HCF of 673, 389, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 389, 257 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 389, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.