How to Find GCF of 378/920, 6740/780?

GCF of 378/920, 6740/780

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 378/920, 6740/780 i.e 2/35880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/920, 6740/780.

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 378/920,6740/780?

Given fractions are 378/920,6740/780

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 378/920,6740/780, numerators are 378,6740

Denominators are 920,780

The GCF of 378,6740 is 2 .

LCM of 920,780 is 35880.

The greatest common factor of 378/920,6740/780 = [GCF of 378,6740]/[LCM of 920,780]= 2/35880

Therefore, the GCF of 378/920,6740/780 is 2/35880.

Greatest Common Factor of 378,6740

To find the highest common factor of 378,6740, we have to find the factors of both numbers and list the highest common factor.

The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378

The factors of 6740 are 1, 2, 4, 5, 10, 20, 337, 674, 1348, 1685, 3370, 6740

The HCF of 378,6740 is 2.

Lets's calculate GCF of 378,6740

Greatest Common Factor (GCF) of 378,6740 By Common Division

2	378, 6740
	189, 3370

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

Greatest Common Factor of 378,6740 By Matching Biggest Common Factor Method

Now, list down the factors of 378

1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378

Now, list down the factors of 6740

1,2,4,5,10,20,337,674,1348,1685,3370,6740

Greatest Common Factor

We found the factors 378,6740 . The biggest common factor number is the GCF number.
So the greatest common factor 378,6740 is 2.

Lets's calculate LCM of 920,780

Lowest Common Multiple of 920,780 using Common Division

2	920, 780
2	460, 390
5	230, 195
	46, 39

∴ So the LCM of the given numbers is 2 x 2 x 5 x 46 x 39 = 35880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35880

Therefore, the GCF of Fractions 378/920,6740/780 is 2/35880

Least Common Multiple of 920,780 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 920,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(920,780) = 20

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

GCF(920,780) x common factors =20 x 1 = 20

LCM(920,780) = ( 920 × 780 ) / 20

LCM(920,780) = 717600 / 20

LCM(920,780) = 35880

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FAQs on GCF of Fractions of 378/920, 6740/780

1. What is the HCF of 378,6740?

The HCF of 378,6740 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 378/920, 6740/780?

Answer: GCF of Numerators as per given numbers 378/920, 6740/780 is

GCF of Numerators i.e. for 378,6740 is 2

LCM of denominators i.e. for 920,780 is 35880.

Thus, GCF of Fractions is 2/35880.Finally, GCF of Fractions for 378/920, 6740/780 is 2/35880.