Greatest Common Factor of 3/78, 14/35, 72/364, 128/660

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 3/78, 14/35, 72/364, 128/660

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 3/78,14/35,72/364,128/660

Given fractions are 3/78,14/35,72/364,128/660

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 3,14,72,128

Greatest Common Factor of Numerators i.e. GCF of 3,14,72,128 is 1 .

LCM of Denominators means LCM of 78,35,364,660 as per the given fractions.

LCM of 78,35,364,660 is 60060 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 3,14,72,128

GCF of Fractions 3/78,14/35,72/364,128/660 is 1/60060

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

Greatest Common Factor of 3,14,72,128 By Matching Biggest Common Factor Method

Greatest Common Factor of 3,14,72,128 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 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

Factors of 128

List of positive integer factors of 128 that divides 128 without a remainder.

1,2,4,8,16,32,64,128

Greatest Common Factor

We found the factors 3,14,72,128 . The biggest common factor number is the GCF number.
So the greatest common factor 3,14,72,128 is 1.

Lets's calculate LCM of 78,35,364,660

2 78, 35, 364, 660
2 39, 35, 182, 330
3 39, 35, 91, 165
5 13, 35, 91, 55
7 13, 7, 91, 11
13 13, 1, 13, 11
1, 1, 1, 11

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 13 x 1 x 1 x 1 x 11 = 60060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/60060

Therefore, the GCF of Fractions 3/78,14/35,72/364,128/660 is 1/60060

Least Common Multiple of 78,35,364,660 with GCF Formula

Least Common Multiple of 78,35,364,660 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 78,35,364,660 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,35,364,660) = 1

common factors(in case of two or more numbers have common factors) = 10920

GCF(78,35,364,660) x common factors =1 x 10920 = 10920

LCM(78,35,364,660) = ( 78 × 35 × 364 × 660 ) / 10920

LCM(78,35,364,660) = 655855200 / 10920

LCM(78,35,364,660) = 60060


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 3/78, 14/35, 72/364, 128/660

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 3/78, 14/35, 72/364, 128/660?

Answer: GCF of Numerators as per given numbers 3/78, 14/35, 72/364, 128/660 is

GCF of Numerators i.e. for 3,14,72,128 is 1

LCM of denominators i.e. for 78,35,364,660 is 60060.

Thus, GCF of Fractions is 1/60060.Finally, GCF of Fractions for 3/78, 14/35, 72/364, 128/660 is 1/60060.