How to Find GCF of 30/39, 56/60, 54/12?

GCF of 30/39, 56/60, 54/12

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 30/39, 56/60, 54/12 i.e 2/780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/39, 56/60, 54/12.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 30/39,56/60,54/12?

Given fractions are 30/39,56/60,54/12

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 30/39,56/60,54/12, numerators are 30,56,54

Denominators are 39,60,12

The GCF of 30,56,54 is 2 .

LCM of 39,60,12 is 780.

The greatest common factor of 30/39,56/60,54/12 = [GCF of 30,56,54]/[LCM of 39,60,12]= 2/780

Therefore, the GCF of 30/39,56/60,54/12 is 2/780.

Greatest Common Factor of 30,56,54

To find the highest common factor of 30,56,54, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The HCF of 30,56,54 is 2.

Lets's calculate GCF of 30,56,54

Greatest Common Factor (GCF) of 30,56,54 By Common Division

2	30, 56, 54
	15, 28, 27

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 30,56,54 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 56

1,2,4,7,8,14,28,56

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Greatest Common Factor

We found the factors 30,56,54 . The biggest common factor number is the GCF number.
So the greatest common factor 30,56,54 is 2.

Lets's calculate LCM of 39,60,12

Lowest Common Multiple of 39,60,12 using Common Division

2	39, 60, 12
2	39, 30, 6
3	39, 15, 3
	13, 5, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 5 x 1 = 780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/780

Therefore, the GCF of Fractions 30/39,56/60,54/12 is 2/780

Least Common Multiple of 39,60,12 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 39,60,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(39,60,12) = 3

common factors(in case of two or more numbers have common factors) = 12

GCF(39,60,12) x common factors =3 x 12 = 36

LCM(39,60,12) = ( 39 × 60 × 12 ) / 36

LCM(39,60,12) = 28080 / 36

LCM(39,60,12) = 780

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 30/39, 56/60, 54/12

1. What is the HCF of 30,56,54?

The HCF of 30,56,54 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 30/39, 56/60, 54/12?

Answer: GCF of Numerators as per given numbers 30/39, 56/60, 54/12 is

GCF of Numerators i.e. for 30,56,54 is 2

LCM of denominators i.e. for 39,60,12 is 780.

Thus, GCF of Fractions is 2/780.Finally, GCF of Fractions for 30/39, 56/60, 54/12 is 2/780.