Greatest Common Factor of 214/50, 189/56, 448/78

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 214/50, 189/56, 448/78

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 214/50,189/56,448/78

Given fractions are 214/50,189/56,448/78

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 214,189,448

Greatest Common Factor of Numerators i.e. GCF of 214,189,448 is 1 .

LCM of Denominators means LCM of 50,56,78 as per the given fractions.

LCM of 50,56,78 is 54600 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 214,189,448

GCF of Fractions 214/50,189/56,448/78 is 1/54600

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 214,189,448 By Matching Biggest Common Factor Method

Greatest Common Factor of 214,189,448 By Matching Biggest Common Factor Method

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1,2,107,214

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1,3,7,9,21,27,63,189

Factors of 448

List of positive integer factors of 448 that divides 448 without a remainder.

1,2,4,7,8,14,16,28,32,56,64,112,224,448

Greatest Common Factor

We found the factors 214,189,448 . The biggest common factor number is the GCF number.
So the greatest common factor 214,189,448 is 1.

Lets's calculate LCM of 50,56,78

2 50, 56, 78
25, 28, 39

∴ So the LCM of the given numbers is 2 x 25 x 28 x 39 = 54600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/54600

Therefore, the GCF of Fractions 214/50,189/56,448/78 is 1/54600

Least Common Multiple of 50,56,78 with GCF Formula

Least Common Multiple of 50,56,78 with GCF Formula

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

We need to calculate greatest common factor of 50,56,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(50,56,78) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(50,56,78) x common factors =2 x 2 = 4

LCM(50,56,78) = ( 50 × 56 × 78 ) / 4

LCM(50,56,78) = 218400 / 4

LCM(50,56,78) = 54600


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 214/50, 189/56, 448/78

1. 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.

2. What is the GCF of Fractions for 214/50, 189/56, 448/78?

Answer: GCF of Numerators as per given numbers 214/50, 189/56, 448/78 is

GCF of Numerators i.e. for 214,189,448 is 1

LCM of denominators i.e. for 50,56,78 is 54600.

Thus, GCF of Fractions is 1/54600.Finally, GCF of Fractions for 214/50, 189/56, 448/78 is 1/54600.