How to Find GCF of 812/978, 1936/6284?

GCF of 812/978, 1936/6284

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 812/978, 1936/6284 i.e 4/3072876 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/978, 1936/6284.

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 812/978,1936/6284?

Given fractions are 812/978,1936/6284

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 812/978,1936/6284, numerators are 812,1936

Denominators are 978,6284

The GCF of 812,1936 is 4 .

LCM of 978,6284 is 3072876.

The greatest common factor of 812/978,1936/6284 = [GCF of 812,1936]/[LCM of 978,6284]= 4/3072876

Therefore, the GCF of 812/978,1936/6284 is 4/3072876.

Greatest Common Factor of 812,1936

To find the highest common factor of 812,1936, we have to find the factors of both numbers and list the highest common factor.

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The factors of 1936 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 121, 176, 242, 484, 968, 1936

The HCF of 812,1936 is 4.

Lets's calculate GCF of 812,1936

Greatest Common Factor (GCF) of 812,1936 By Common Division

2	812, 1936
2	406, 968
	203, 484

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 812,1936 By Matching Biggest Common Factor Method

Now, list down the factors of 812

1,2,4,7,14,28,29,58,116,203,406,812

Now, list down the factors of 1936

1,2,4,8,11,16,22,44,88,121,176,242,484,968,1936

Greatest Common Factor

We found the factors 812,1936 . The biggest common factor number is the GCF number.
So the greatest common factor 812,1936 is 4.

Lets's calculate LCM of 978,6284

Lowest Common Multiple of 978,6284 using Common Division

2	978, 6284
	489, 3142

∴ So the LCM of the given numbers is 2 x 489 x 3142 = 3072876

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3072876

Therefore, the GCF of Fractions 812/978,1936/6284 is 4/3072876

Least Common Multiple of 978,6284 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 978,6284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,6284) = 2

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

GCF(978,6284) x common factors =2 x 1 = 2

LCM(978,6284) = ( 978 × 6284 ) / 2

LCM(978,6284) = 6145752 / 2

LCM(978,6284) = 3072876

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 812/978, 1936/6284

1. What is the HCF of 812,1936?

The HCF of 812,1936 is 4

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 812/978, 1936/6284?

Answer: GCF of Numerators as per given numbers 812/978, 1936/6284 is

GCF of Numerators i.e. for 812,1936 is 4

LCM of denominators i.e. for 978,6284 is 3072876.

Thus, GCF of Fractions is 4/3072876.Finally, GCF of Fractions for 812/978, 1936/6284 is 4/3072876.