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GCF of 138/90, 314/433

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 138/90, 314/433 i.e 2/38970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/90, 314/433.

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 138/90,314/433?

Given fractions are 138/90,314/433

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 138/90,314/433, numerators are 138,314

Denominators are 90,433

The GCF of 138,314 is 2 .

LCM of 90,433 is 38970.

The greatest common factor of 138/90,314/433 = [GCF of 138,314]/[LCM of 90,433]= 2/38970

Therefore, the GCF of 138/90,314/433 is 2/38970.

Greatest Common Factor of 138,314

To find the highest common factor of 138,314, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 314 are 1, 2, 157, 314

The HCF of 138,314 is 2.

Lets's calculate GCF of 138,314

Greatest Common Factor (GCF) of 138,314 By Common Division

2 138, 314
69, 157

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

Greatest Common Factor of 138,314 By Matching Biggest Common Factor Method

Greatest Common Factor of 138,314 By Matching Biggest Common Factor Method

Now, list down the factors of 138

:

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

Now, list down the factors of 314

:

1,2,157,314

Greatest Common Factor

We found the factors 138,314 . The biggest common factor number is the GCF number.
So the greatest common factor 138,314 is 2.

Lets's calculate LCM of 90,433

Lowest Common Multiple of 90,433 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 38970

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38970

Therefore, the GCF of Fractions 138/90,314/433 is 2/38970

Least Common Multiple of 90,433 with GCF Formula

Least Common Multiple of 90,433 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 90,433 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(90,433) = 1

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

GCF(90,433) x common factors =1 x 1 = 1

LCM(90,433) = ( 90 × 433 ) / 1

LCM(90,433) = 38970 / 1

LCM(90,433) = 38970


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FAQs on GCF of Fractions of 138/90, 314/433

1. What is the HCF of 138,314?

The HCF of 138,314 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 138/90, 314/433?

Answer: GCF of Numerators as per given numbers 138/90, 314/433 is

GCF of Numerators i.e. for 138,314 is 2

LCM of denominators i.e. for 90,433 is 38970.

Thus, GCF of Fractions is 2/38970.Finally, GCF of Fractions for 138/90, 314/433 is 2/38970.