Highest Common Factor of 673, 380, 993 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, 380, 993 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 380, 993 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, 380, 993 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, 380, 993 is 1.

HCF(673, 380, 993) = 1

HCF of 673, 380, 993 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, 380, 993 is 1.

Highest Common Factor of 673,380,993 using Euclid's algorithm

Highest Common Factor of 673,380,993 is 1

Step 1: Since 673 > 380, we apply the division lemma to 673 and 380, to get

673 = 380 x 1 + 293

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 293 and 380, to get

380 = 293 x 1 + 87

Step 3: We consider the new divisor 293 and the new remainder 87, and apply the division lemma to get

293 = 87 x 3 + 32

We consider the new divisor 87 and the new remainder 32,and apply the division lemma to get

87 = 32 x 2 + 23

We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get

32 = 23 x 1 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 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 673 and 380 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(87,32) = HCF(293,87) = HCF(380,293) = HCF(673,380) .

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

Step 1: Since 993 > 1, we apply the division lemma to 993 and 1, to get

993 = 1 x 993 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 993 is 1

Notice that 1 = HCF(993,1) .

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, 380, 993 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, 380, 993?

Answer: HCF of 673, 380, 993 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 380, 993 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 380, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.