Greatest Common Factor of 217/154, 9734/1368

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 217/154, 9734/1368

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 217/154,9734/1368

Given fractions are 217/154,9734/1368

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 217,9734

Greatest Common Factor of Numerators i.e. GCF of 217,9734 is 31 .

LCM of Denominators means LCM of 154,1368 as per the given fractions.

LCM of 154,1368 is 105336 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 217,9734

GCF of Fractions 217/154,9734/1368 is 31/105336

31 217, 9734
7, 314

∴ So the GCF of the given numbers is 31 = 31

Greatest Common Factor of 217,9734 By Matching Biggest Common Factor Method

Greatest Common Factor of 217,9734 By Matching Biggest Common Factor Method

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1,7,31,217

Factors of 9734

List of positive integer factors of 9734 that divides 9734 without a remainder.

1,2,31,62,157,314,4867,9734

Greatest Common Factor

We found the factors 217,9734 . The biggest common factor number is the GCF number.
So the greatest common factor 217,9734 is 31.

Lets's calculate LCM of 154,1368

2 154, 1368
77, 684

∴ So the LCM of the given numbers is 2 x 77 x 684 = 105336

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/105336

Therefore, the GCF of Fractions 217/154,9734/1368 is 31/105336

Least Common Multiple of 154,1368 with GCF Formula

Least Common Multiple of 154,1368 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 154,1368 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(154,1368) = 2

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

GCF(154,1368) x common factors =2 x 1 = 2

LCM(154,1368) = ( 154 × 1368 ) / 2

LCM(154,1368) = 210672 / 2

LCM(154,1368) = 105336


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 217/154, 9734/1368

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 217/154, 9734/1368?

Answer: GCF of Numerators as per given numbers 217/154, 9734/1368 is

GCF of Numerators i.e. for 217,9734 is 31

LCM of denominators i.e. for 154,1368 is 105336.

Thus, GCF of Fractions is 31/105336.Finally, GCF of Fractions for 217/154, 9734/1368 is 31/105336.