Greatest Common Factor of 9/27, 1/84, 78/32, 96/714

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 9/27, 1/84, 78/32, 96/714

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 9/27,1/84,78/32,96/714

Given fractions are 9/27,1/84,78/32,96/714

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 9,1,78,96

Greatest Common Factor of Numerators i.e. GCF of 9,1,78,96 is 1 .

LCM of Denominators means LCM of 27,84,32,714 as per the given fractions.

LCM of 27,84,32,714 is 102816 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 9,1,78,96

GCF of Fractions 9/27,1/84,78/32,96/714 is 1/102816

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

Greatest Common Factor of 9,1,78,96 By Matching Biggest Common Factor Method

Greatest Common Factor of 9,1,78,96 By Matching Biggest Common Factor Method

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1,3,9

Factors of 1

List of positive integer factors of 1 that divides 1 without a remainder.

1

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Factors of 96

List of positive integer factors of 96 that divides 96 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,96

Greatest Common Factor

We found the factors 9,1,78,96 . The biggest common factor number is the GCF number.
So the greatest common factor 9,1,78,96 is 1.

Lets's calculate LCM of 27,84,32,714

2 27, 84, 32, 714
2 27, 42, 16, 357
3 27, 21, 8, 357
7 9, 7, 8, 119
9, 1, 8, 17

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 9 x 1 x 8 x 17 = 102816

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102816

Therefore, the GCF of Fractions 9/27,1/84,78/32,96/714 is 1/102816

Least Common Multiple of 27,84,32,714 with GCF Formula

Least Common Multiple of 27,84,32,714 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 27,84,32,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,84,32,714) = 1

common factors(in case of two or more numbers have common factors) = 504

GCF(27,84,32,714) x common factors =1 x 504 = 504

LCM(27,84,32,714) = ( 27 × 84 × 32 × 714 ) / 504

LCM(27,84,32,714) = 51819264 / 504

LCM(27,84,32,714) = 102816


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 9/27, 1/84, 78/32, 96/714

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 9/27, 1/84, 78/32, 96/714?

Answer: GCF of Numerators as per given numbers 9/27, 1/84, 78/32, 96/714 is

GCF of Numerators i.e. for 9,1,78,96 is 1

LCM of denominators i.e. for 27,84,32,714 is 102816.

Thus, GCF of Fractions is 1/102816.Finally, GCF of Fractions for 9/27, 1/84, 78/32, 96/714 is 1/102816.