Greatest Common Factor of 3/14, 4/97, 7/84, 78/216

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 3/14, 4/97, 7/84, 78/216

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 3/14,4/97,7/84,78/216

Given fractions are 3/14,4/97,7/84,78/216

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 3,4,7,78

Greatest Common Factor of Numerators i.e. GCF of 3,4,7,78 is 1 .

LCM of Denominators means LCM of 14,97,84,216 as per the given fractions.

LCM of 14,97,84,216 is 146664 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 3,4,7,78

GCF of Fractions 3/14,4/97,7/84,78/216 is 1/146664

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

Greatest Common Factor of 3,4,7,78 By Matching Biggest Common Factor Method

Greatest Common Factor of 3,4,7,78 By Matching Biggest Common Factor Method

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1,3

Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1,2,4

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1,7

Factors of 78

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

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

Greatest Common Factor

We found the factors 3,4,7,78 . The biggest common factor number is the GCF number.
So the greatest common factor 3,4,7,78 is 1.

Lets's calculate LCM of 14,97,84,216

2 14, 97, 84, 216
2 7, 97, 42, 108
3 7, 97, 21, 54
7 7, 97, 7, 18
1, 97, 1, 18

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 97 x 1 x 18 = 146664

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/146664

Therefore, the GCF of Fractions 3/14,4/97,7/84,78/216 is 1/146664

Least Common Multiple of 14,97,84,216 with GCF Formula

Least Common Multiple of 14,97,84,216 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 14,97,84,216 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,97,84,216) = 1

common factors(in case of two or more numbers have common factors) = 168

GCF(14,97,84,216) x common factors =1 x 168 = 168

LCM(14,97,84,216) = ( 14 × 97 × 84 × 216 ) / 168

LCM(14,97,84,216) = 24639552 / 168

LCM(14,97,84,216) = 146664


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 3/14, 4/97, 7/84, 78/216

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 3/14, 4/97, 7/84, 78/216?

Answer: GCF of Numerators as per given numbers 3/14, 4/97, 7/84, 78/216 is

GCF of Numerators i.e. for 3,4,7,78 is 1

LCM of denominators i.e. for 14,97,84,216 is 146664.

Thus, GCF of Fractions is 1/146664.Finally, GCF of Fractions for 3/14, 4/97, 7/84, 78/216 is 1/146664.