How to Find GCF of 774/614, 2314/978?

GCF of 774/614, 2314/978

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 774/614, 2314/978 i.e 2/300246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 774/614, 2314/978.

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 774/614,2314/978?

Given fractions are 774/614,2314/978

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 774/614,2314/978, numerators are 774,2314

Denominators are 614,978

The GCF of 774,2314 is 2 .

LCM of 614,978 is 300246.

The greatest common factor of 774/614,2314/978 = [GCF of 774,2314]/[LCM of 614,978]= 2/300246

Therefore, the GCF of 774/614,2314/978 is 2/300246.

Greatest Common Factor of 774,2314

To find the highest common factor of 774,2314, we have to find the factors of both numbers and list the highest common factor.

The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774

The factors of 2314 are 1, 2, 13, 26, 89, 178, 1157, 2314

The HCF of 774,2314 is 2.

Lets's calculate GCF of 774,2314

Greatest Common Factor (GCF) of 774,2314 By Common Division

2	774, 2314
	387, 1157

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

Greatest Common Factor of 774,2314 By Matching Biggest Common Factor Method

Now, list down the factors of 774

1,2,3,6,9,18,43,86,129,258,387,774

Now, list down the factors of 2314

1,2,13,26,89,178,1157,2314

Greatest Common Factor

We found the factors 774,2314 . The biggest common factor number is the GCF number.
So the greatest common factor 774,2314 is 2.

Lets's calculate LCM of 614,978

Lowest Common Multiple of 614,978 using Common Division

2	614, 978
	307, 489

∴ So the LCM of the given numbers is 2 x 307 x 489 = 300246

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/300246

Therefore, the GCF of Fractions 774/614,2314/978 is 2/300246

Least Common Multiple of 614,978 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 614,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,978) = 2

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

GCF(614,978) x common factors =2 x 1 = 2

LCM(614,978) = ( 614 × 978 ) / 2

LCM(614,978) = 600492 / 2

LCM(614,978) = 300246

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 774/614, 2314/978

1. What is the HCF of 774,2314?

The HCF of 774,2314 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 774/614, 2314/978?

Answer: GCF of Numerators as per given numbers 774/614, 2314/978 is

GCF of Numerators i.e. for 774,2314 is 2

LCM of denominators i.e. for 614,978 is 300246.

Thus, GCF of Fractions is 2/300246.Finally, GCF of Fractions for 774/614, 2314/978 is 2/300246.