How to Find GCF of 78/612, 28/758, 214/785?

GCF of 78/612, 28/758, 214/785

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 78/612, 28/758, 214/785 i.e 2/182079180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/612, 28/758, 214/785.

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 78/612,28/758,214/785?

Given fractions are 78/612,28/758,214/785

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 78/612,28/758,214/785, numerators are 78,28,214

Denominators are 612,758,785

The GCF of 78,28,214 is 2 .

LCM of 612,758,785 is 182079180.

The greatest common factor of 78/612,28/758,214/785 = [GCF of 78,28,214]/[LCM of 612,758,785]= 2/182079180

Therefore, the GCF of 78/612,28/758,214/785 is 2/182079180.

Greatest Common Factor of 78,28,214

To find the highest common factor of 78,28,214, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

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

The factors of 214 are 1, 2, 107, 214

The HCF of 78,28,214 is 2.

Lets's calculate GCF of 78,28,214

Greatest Common Factor (GCF) of 78,28,214 By Common Division

2	78, 28, 214
	39, 14, 107

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

Greatest Common Factor of 78,28,214 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 214

1,2,107,214

Greatest Common Factor

We found the factors 78,28,214 . The biggest common factor number is the GCF number.
So the greatest common factor 78,28,214 is 2.

Lets's calculate LCM of 612,758,785

Lowest Common Multiple of 612,758,785 using Common Division

2	612, 758, 785
	306, 379, 785

∴ So the LCM of the given numbers is 2 x 306 x 379 x 785 = 182079180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/182079180

Therefore, the GCF of Fractions 78/612,28/758,214/785 is 2/182079180

Least Common Multiple of 612,758,785 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 612,758,785 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(612,758,785) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(612,758,785) x common factors =1 x 2 = 2

LCM(612,758,785) = ( 612 × 758 × 785 ) / 2

LCM(612,758,785) = 364158360 / 2

LCM(612,758,785) = 182079180

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 78/612, 28/758, 214/785

1. What is the HCF of 78,28,214?

The HCF of 78,28,214 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 78/612, 28/758, 214/785?

Answer: GCF of Numerators as per given numbers 78/612, 28/758, 214/785 is

GCF of Numerators i.e. for 78,28,214 is 2

LCM of denominators i.e. for 612,758,785 is 182079180.

Thus, GCF of Fractions is 2/182079180.Finally, GCF of Fractions for 78/612, 28/758, 214/785 is 2/182079180.