How to Find GCF of 540/379, 516/978?

GCF of 540/379, 516/978

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 540/379, 516/978 i.e 12/370662 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/379, 516/978.

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 540/379,516/978?

Given fractions are 540/379,516/978

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 540/379,516/978, numerators are 540,516

Denominators are 379,978

The GCF of 540,516 is 12 .

LCM of 379,978 is 370662.

The greatest common factor of 540/379,516/978 = [GCF of 540,516]/[LCM of 379,978]= 12/370662

Therefore, the GCF of 540/379,516/978 is 12/370662.

Greatest Common Factor of 540,516

To find the highest common factor of 540,516, we have to find the factors of both numbers and list the highest common factor.

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516

The HCF of 540,516 is 12.

Lets's calculate GCF of 540,516

Greatest Common Factor (GCF) of 540,516 By Common Division

2	540, 516
2	270, 258
3	135, 129
	45, 43

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 540,516 By Matching Biggest Common Factor Method

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Now, list down the factors of 516

1,2,3,4,6,12,43,86,129,172,258,516

Greatest Common Factor

We found the factors 540,516 . The biggest common factor number is the GCF number.
So the greatest common factor 540,516 is 12.

Lets's calculate LCM of 379,978

Lowest Common Multiple of 379,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 370662

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/370662

Therefore, the GCF of Fractions 540/379,516/978 is 12/370662

Least Common Multiple of 379,978 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 379,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(379,978) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(379,978) x common factors =1 x 1 = 1

LCM(379,978) = ( 379 × 978 ) / 1

LCM(379,978) = 370662 / 1

LCM(379,978) = 370662

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 540/379, 516/978

1. What is the HCF of 540,516?

The HCF of 540,516 is 12

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 540/379, 516/978?

Answer: GCF of Numerators as per given numbers 540/379, 516/978 is

GCF of Numerators i.e. for 540,516 is 12

LCM of denominators i.e. for 379,978 is 370662.

Thus, GCF of Fractions is 12/370662.Finally, GCF of Fractions for 540/379, 516/978 is 12/370662.