Greatest Common Factor of 800/78, 196/69, 254/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 800/78, 196/69, 254/14

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 800/78,196/69,254/14

Given fractions are 800/78,196/69,254/14

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 800,196,254

Greatest Common Factor of Numerators i.e. GCF of 800,196,254 is 2 .

LCM of Denominators means LCM of 78,69,14 as per the given fractions.

LCM of 78,69,14 is 12558 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 800,196,254

GCF of Fractions 800/78,196/69,254/14 is 2/12558

2 800, 196, 254
400, 98, 127

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 800,196,254 By Matching Biggest Common Factor Method

Greatest Common Factor of 800,196,254 By Matching Biggest Common Factor Method

Factors of 800

List of positive integer factors of 800 that divides 800 without a remainder.

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

Factors of 196

List of positive integer factors of 196 that divides 196 without a remainder.

1,2,4,7,14,28,49,98,196

Factors of 254

List of positive integer factors of 254 that divides 254 without a remainder.

1,2,127,254

Greatest Common Factor

We found the factors 800,196,254 . The biggest common factor number is the GCF number.
So the greatest common factor 800,196,254 is 2.

Lets's calculate LCM of 78,69,14

2 78, 69, 14
3 39, 69, 7
13, 23, 7

∴ So the LCM of the given numbers is 2 x 3 x 13 x 23 x 7 = 12558

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12558

Therefore, the GCF of Fractions 800/78,196/69,254/14 is 2/12558

Least Common Multiple of 78,69,14 with GCF Formula

Least Common Multiple of 78,69,14 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 78,69,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,69,14) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(78,69,14) x common factors =1 x 6 = 6

LCM(78,69,14) = ( 78 × 69 × 14 ) / 6

LCM(78,69,14) = 75348 / 6

LCM(78,69,14) = 12558


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 800/78, 196/69, 254/14

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 800/78, 196/69, 254/14?

Answer: GCF of Numerators as per given numbers 800/78, 196/69, 254/14 is

GCF of Numerators i.e. for 800,196,254 is 2

LCM of denominators i.e. for 78,69,14 is 12558.

Thus, GCF of Fractions is 2/12558.Finally, GCF of Fractions for 800/78, 196/69, 254/14 is 2/12558.