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GCF of 180/208, 338/512

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 180/208, 338/512 i.e 2/6656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/208, 338/512.

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 180/208,338/512?

Given fractions are 180/208,338/512

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 180/208,338/512, numerators are 180,338

Denominators are 208,512

The GCF of 180,338 is 2 .

LCM of 208,512 is 6656.

The greatest common factor of 180/208,338/512 = [GCF of 180,338]/[LCM of 208,512]= 2/6656

Therefore, the GCF of 180/208,338/512 is 2/6656.

Greatest Common Factor of 180,338

To find the highest common factor of 180,338, we have to find the factors of both numbers and list the highest common factor.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 338 are 1, 2, 13, 26, 169, 338

The HCF of 180,338 is 2.

Lets's calculate GCF of 180,338

Greatest Common Factor (GCF) of 180,338 By Common Division

2 180, 338
90, 169

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

Greatest Common Factor of 180,338 By Matching Biggest Common Factor Method

Greatest Common Factor of 180,338 By Matching Biggest Common Factor Method

Now, list down the factors of 180

:

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Now, list down the factors of 338

:

1,2,13,26,169,338

Greatest Common Factor

We found the factors 180,338 . The biggest common factor number is the GCF number.
So the greatest common factor 180,338 is 2.

Lets's calculate LCM of 208,512

Lowest Common Multiple of 208,512 using Common Division

2 208, 512
2 104, 256
2 52, 128
2 26, 64
13, 32

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 13 x 32 = 6656

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6656

Therefore, the GCF of Fractions 180/208,338/512 is 2/6656

Least Common Multiple of 208,512 with GCF Formula

Least Common Multiple of 208,512 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 208,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,512) = 16

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

GCF(208,512) x common factors =16 x 1 = 16

LCM(208,512) = ( 208 × 512 ) / 16

LCM(208,512) = 106496 / 16

LCM(208,512) = 6656


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FAQs on GCF of Fractions of 180/208, 338/512

1. What is the HCF of 180,338?

The HCF of 180,338 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 180/208, 338/512?

Answer: GCF of Numerators as per given numbers 180/208, 338/512 is

GCF of Numerators i.e. for 180,338 is 2

LCM of denominators i.e. for 208,512 is 6656.

Thus, GCF of Fractions is 2/6656.Finally, GCF of Fractions for 180/208, 338/512 is 2/6656.