Greatest Common Factor of 20/30, 28/34, 32/56, 67/60

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 20/30, 28/34, 32/56, 67/60

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 20/30,28/34,32/56,67/60

Given fractions are 20/30,28/34,32/56,67/60

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 20,28,32,67

Greatest Common Factor of Numerators i.e. GCF of 20,28,32,67 is 1 .

LCM of Denominators means LCM of 30,34,56,60 as per the given fractions.

LCM of 30,34,56,60 is 14280 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 20,28,32,67

GCF of Fractions 20/30,28/34,32/56,67/60 is 1/14280

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

Greatest Common Factor of 20,28,32,67 By Matching Biggest Common Factor Method

Greatest Common Factor of 20,28,32,67 By Matching Biggest Common Factor Method

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Factors of 28

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Greatest Common Factor

We found the factors 20,28,32,67 . The biggest common factor number is the GCF number.
So the greatest common factor 20,28,32,67 is 1.

Lets's calculate LCM of 30,34,56,60

2 30, 34, 56, 60
2 15, 17, 28, 30
3 15, 17, 14, 15
5 5, 17, 14, 5
1, 17, 14, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 17 x 14 x 1 = 14280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14280

Therefore, the GCF of Fractions 20/30,28/34,32/56,67/60 is 1/14280

Least Common Multiple of 30,34,56,60 with GCF Formula

Least Common Multiple of 30,34,56,60 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 30,34,56,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,34,56,60) = 2

common factors(in case of two or more numbers have common factors) = 120

GCF(30,34,56,60) x common factors =2 x 120 = 240

LCM(30,34,56,60) = ( 30 × 34 × 56 × 60 ) / 240

LCM(30,34,56,60) = 3427200 / 240

LCM(30,34,56,60) = 14280


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 20/30, 28/34, 32/56, 67/60

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 20/30, 28/34, 32/56, 67/60?

Answer: GCF of Numerators as per given numbers 20/30, 28/34, 32/56, 67/60 is

GCF of Numerators i.e. for 20,28,32,67 is 1

LCM of denominators i.e. for 30,34,56,60 is 14280.

Thus, GCF of Fractions is 1/14280.Finally, GCF of Fractions for 20/30, 28/34, 32/56, 67/60 is 1/14280.