How to Find GCF of 38/306, 78/950, 298/412?

GCF of 38/306, 78/950, 298/412

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 38/306, 78/950, 298/412 i.e 2/29942100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/306, 78/950, 298/412.

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 38/306,78/950,298/412?

Given fractions are 38/306,78/950,298/412

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 38/306,78/950,298/412, numerators are 38,78,298

Denominators are 306,950,412

The GCF of 38,78,298 is 2 .

LCM of 306,950,412 is 29942100.

The greatest common factor of 38/306,78/950,298/412 = [GCF of 38,78,298]/[LCM of 306,950,412]= 2/29942100

Therefore, the GCF of 38/306,78/950,298/412 is 2/29942100.

Greatest Common Factor of 38,78,298

To find the highest common factor of 38,78,298, we have to find the factors of both numbers and list the highest common factor.

The factors of 38 are 1, 2, 19, 38

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

The factors of 298 are 1, 2, 149, 298

The HCF of 38,78,298 is 2.

Lets's calculate GCF of 38,78,298

Greatest Common Factor (GCF) of 38,78,298 By Common Division

2	38, 78, 298
	19, 39, 149

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

Greatest Common Factor of 38,78,298 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 78

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

Now, list down the factors of 298

1,2,149,298

Greatest Common Factor

We found the factors 38,78,298 . The biggest common factor number is the GCF number.
So the greatest common factor 38,78,298 is 2.

Lets's calculate LCM of 306,950,412

Lowest Common Multiple of 306,950,412 using Common Division

2	306, 950, 412
	153, 475, 206

∴ So the LCM of the given numbers is 2 x 153 x 475 x 206 = 29942100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29942100

Therefore, the GCF of Fractions 38/306,78/950,298/412 is 2/29942100

Least Common Multiple of 306,950,412 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 306,950,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(306,950,412) = 2

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

GCF(306,950,412) x common factors =2 x 2 = 4

LCM(306,950,412) = ( 306 × 950 × 412 ) / 4

LCM(306,950,412) = 119768400 / 4

LCM(306,950,412) = 29942100

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 38/306, 78/950, 298/412

1. What is the HCF of 38,78,298?

The HCF of 38,78,298 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 38/306, 78/950, 298/412?

Answer: GCF of Numerators as per given numbers 38/306, 78/950, 298/412 is

GCF of Numerators i.e. for 38,78,298 is 2

LCM of denominators i.e. for 306,950,412 is 29942100.

Thus, GCF of Fractions is 2/29942100.Finally, GCF of Fractions for 38/306, 78/950, 298/412 is 2/29942100.