How to Find GCF of 38/13, 137/78, 298/686?

GCF of 38/13, 137/78, 298/686

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 38/13, 137/78, 298/686 i.e 1/26754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/13, 137/78, 298/686.

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 38/13,137/78,298/686?

Given fractions are 38/13,137/78,298/686

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 38/13,137/78,298/686, numerators are 38,137,298

Denominators are 13,78,686

The GCF of 38,137,298 is 1 .

LCM of 13,78,686 is 26754.

The greatest common factor of 38/13,137/78,298/686 = [GCF of 38,137,298]/[LCM of 13,78,686]= 1/26754

Therefore, the GCF of 38/13,137/78,298/686 is 1/26754.

Greatest Common Factor of 38,137,298

To find the highest common factor of 38,137,298, 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 137 are 1, 137

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

The HCF of 38,137,298 is 1.

Lets's calculate GCF of 38,137,298

Greatest Common Factor (GCF) of 38,137,298 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 38,137,298 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 137

1,137

Now, list down the factors of 298

1,2,149,298

Greatest Common Factor

We found the factors 38,137,298 . The biggest common factor number is the GCF number.
So the greatest common factor 38,137,298 is 1.

Lets's calculate LCM of 13,78,686

Lowest Common Multiple of 13,78,686 using Common Division

2	13, 78, 686
13	13, 39, 343
	1, 3, 343

∴ So the LCM of the given numbers is 2 x 13 x 1 x 3 x 343 = 26754

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26754

Therefore, the GCF of Fractions 38/13,137/78,298/686 is 1/26754

Least Common Multiple of 13,78,686 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 13,78,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,78,686) = 1

common factors(in case of two or more numbers have common factors) = 26

GCF(13,78,686) x common factors =1 x 26 = 26

LCM(13,78,686) = ( 13 × 78 × 686 ) / 26

LCM(13,78,686) = 695604 / 26

LCM(13,78,686) = 26754

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FAQs on GCF of Fractions of 38/13, 137/78, 298/686

1. What is the HCF of 38,137,298?

The HCF of 38,137,298 is 1

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 38/13, 137/78, 298/686?

Answer: GCF of Numerators as per given numbers 38/13, 137/78, 298/686 is

GCF of Numerators i.e. for 38,137,298 is 1

LCM of denominators i.e. for 13,78,686 is 26754.

Thus, GCF of Fractions is 1/26754.Finally, GCF of Fractions for 38/13, 137/78, 298/686 is 1/26754.