Greatest Common Factor of 160/194, 345/214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 160/194, 345/214

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 160/194,345/214

Given fractions are 160/194,345/214

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 160,345

Greatest Common Factor of Numerators i.e. GCF of 160,345 is 5 .

LCM of Denominators means LCM of 194,214 as per the given fractions.

LCM of 194,214 is 20758 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 160,345

GCF of Fractions 160/194,345/214 is 5/20758

5 160, 345
32, 69

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 160,345 By Matching Biggest Common Factor Method

Greatest Common Factor of 160,345 By Matching Biggest Common Factor Method

Factors of 160

List of positive integer factors of 160 that divides 160 without a remainder.

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

Factors of 345

List of positive integer factors of 345 that divides 345 without a remainder.

1,3,5,15,23,69,115,345

Greatest Common Factor

We found the factors 160,345 . The biggest common factor number is the GCF number.
So the greatest common factor 160,345 is 5.

Lets's calculate LCM of 194,214

2 194, 214
97, 107

∴ So the LCM of the given numbers is 2 x 97 x 107 = 20758

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/20758

Therefore, the GCF of Fractions 160/194,345/214 is 5/20758

Least Common Multiple of 194,214 with GCF Formula

Least Common Multiple of 194,214 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 194,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(194,214) = 2

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

GCF(194,214) x common factors =2 x 1 = 2

LCM(194,214) = ( 194 × 214 ) / 2

LCM(194,214) = 41516 / 2

LCM(194,214) = 20758


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 160/194, 345/214

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 160/194, 345/214?

Answer: GCF of Numerators as per given numbers 160/194, 345/214 is

GCF of Numerators i.e. for 160,345 is 5

LCM of denominators i.e. for 194,214 is 20758.

Thus, GCF of Fractions is 5/20758.Finally, GCF of Fractions for 160/194, 345/214 is 5/20758.