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GCF of 514/13, 138/385

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 514/13, 138/385 i.e 2/5005 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/13, 138/385.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 514/13,138/385?

Given fractions are 514/13,138/385

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 514/13,138/385, numerators are 514,138

Denominators are 13,385

The GCF of 514,138 is 2 .

LCM of 13,385 is 5005.

The greatest common factor of 514/13,138/385 = [GCF of 514,138]/[LCM of 13,385]= 2/5005

Therefore, the GCF of 514/13,138/385 is 2/5005.

Greatest Common Factor of 514,138

To find the highest common factor of 514,138, we have to find the factors of both numbers and list the highest common factor.

The factors of 514 are 1, 2, 257, 514

The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

The HCF of 514,138 is 2.

Lets's calculate GCF of 514,138

Greatest Common Factor (GCF) of 514,138 By Common Division

2 514, 138
257, 69

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

Greatest Common Factor of 514,138 By Matching Biggest Common Factor Method

Greatest Common Factor of 514,138 By Matching Biggest Common Factor Method

Now, list down the factors of 514

:

1,2,257,514

Now, list down the factors of 138

:

1,2,3,6,23,46,69,138

Greatest Common Factor

We found the factors 514,138 . The biggest common factor number is the GCF number.
So the greatest common factor 514,138 is 2.

Lets's calculate LCM of 13,385

Lowest Common Multiple of 13,385 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5005

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5005

Therefore, the GCF of Fractions 514/13,138/385 is 2/5005

Least Common Multiple of 13,385 with GCF Formula

Least Common Multiple of 13,385 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 13,385 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,385) = 1

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

GCF(13,385) x common factors =1 x 1 = 1

LCM(13,385) = ( 13 × 385 ) / 1

LCM(13,385) = 5005 / 1

LCM(13,385) = 5005


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FAQs on GCF of Fractions of 514/13, 138/385

1. What is the HCF of 514,138?

The HCF of 514,138 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 514/13, 138/385?

Answer: GCF of Numerators as per given numbers 514/13, 138/385 is

GCF of Numerators i.e. for 514,138 is 2

LCM of denominators i.e. for 13,385 is 5005.

Thus, GCF of Fractions is 2/5005.Finally, GCF of Fractions for 514/13, 138/385 is 2/5005.