How to Find GCF of 320/173, 800/714?

GCF of 320/173, 800/714

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 320/173, 800/714 i.e 160/123522 easily. The following is the detailed procedure to determine the greatest common factor of fractions 320/173, 800/714.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 320/173,800/714?

Given fractions are 320/173,800/714

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 320/173,800/714, numerators are 320,800

Denominators are 173,714

The GCF of 320,800 is 160 .

LCM of 173,714 is 123522.

The greatest common factor of 320/173,800/714 = [GCF of 320,800]/[LCM of 173,714]= 160/123522

Therefore, the GCF of 320/173,800/714 is 160/123522.

Greatest Common Factor of 320,800

To find the highest common factor of 320,800, we have to find the factors of both numbers and list the highest common factor.

The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800

The HCF of 320,800 is 160.

Lets's calculate GCF of 320,800

Greatest Common Factor (GCF) of 320,800 By Common Division

2	320, 800
2	160, 400
2	80, 200
2	40, 100
2	20, 50
5	10, 25
	2, 5

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 5 = 160

Greatest Common Factor of 320,800 By Matching Biggest Common Factor Method

Now, list down the factors of 320

1,2,4,5,8,10,16,20,32,40,64,80,160,320

Now, list down the factors of 800

1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800

Greatest Common Factor

We found the factors 320,800 . The biggest common factor number is the GCF number.
So the greatest common factor 320,800 is 160.

Lets's calculate LCM of 173,714

Lowest Common Multiple of 173,714 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 123522

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 160/123522

Therefore, the GCF of Fractions 320/173,800/714 is 160/123522

Least Common Multiple of 173,714 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 173,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(173,714) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(173,714) x common factors =1 x 1 = 1

LCM(173,714) = ( 173 × 714 ) / 1

LCM(173,714) = 123522 / 1

LCM(173,714) = 123522

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 320/173, 800/714

1. What is the HCF of 320,800?

The HCF of 320,800 is 160

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 320/173, 800/714?

Answer: GCF of Numerators as per given numbers 320/173, 800/714 is

GCF of Numerators i.e. for 320,800 is 160

LCM of denominators i.e. for 173,714 is 123522.

Thus, GCF of Fractions is 160/123522.Finally, GCF of Fractions for 320/173, 800/714 is 160/123522.