Greatest Common Factor of 214/20, 135/43, 208/160

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 214/20, 135/43, 208/160

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 214/20,135/43,208/160

Given fractions are 214/20,135/43,208/160

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 214,135,208

Greatest Common Factor of Numerators i.e. GCF of 214,135,208 is 1 .

LCM of Denominators means LCM of 20,43,160 as per the given fractions.

LCM of 20,43,160 is 6880 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 214,135,208

GCF of Fractions 214/20,135/43,208/160 is 1/6880

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

Greatest Common Factor of 214,135,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 214,135,208 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 135

List of positive integer factors of 135 that divides 135 without a remainder.

1,3,5,9,15,27,45,135

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 214,135,208 . The biggest common factor number is the GCF number.
So the greatest common factor 214,135,208 is 1.

Lets's calculate LCM of 20,43,160

2 20, 43, 160
2 10, 43, 80
5 5, 43, 40
1, 43, 8

∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 43 x 8 = 6880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6880

Therefore, the GCF of Fractions 214/20,135/43,208/160 is 1/6880

Least Common Multiple of 20,43,160 with GCF Formula

Least Common Multiple of 20,43,160 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 20,43,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,43,160) = 1

common factors(in case of two or more numbers have common factors) = 20

GCF(20,43,160) x common factors =1 x 20 = 20

LCM(20,43,160) = ( 20 × 43 × 160 ) / 20

LCM(20,43,160) = 137600 / 20

LCM(20,43,160) = 6880


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 214/20, 135/43, 208/160

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 214/20, 135/43, 208/160?

Answer: GCF of Numerators as per given numbers 214/20, 135/43, 208/160 is

GCF of Numerators i.e. for 214,135,208 is 1

LCM of denominators i.e. for 20,43,160 is 6880.

Thus, GCF of Fractions is 1/6880.Finally, GCF of Fractions for 214/20, 135/43, 208/160 is 1/6880.