How to Find GCF of 512/338, 400/131?

GCF of 512/338, 400/131

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 512/338, 400/131 i.e 16/44278 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/338, 400/131.

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 512/338,400/131?

Given fractions are 512/338,400/131

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 512/338,400/131, numerators are 512,400

Denominators are 338,131

The GCF of 512,400 is 16 .

LCM of 338,131 is 44278.

The greatest common factor of 512/338,400/131 = [GCF of 512,400]/[LCM of 338,131]= 16/44278

Therefore, the GCF of 512/338,400/131 is 16/44278.

Greatest Common Factor of 512,400

To find the highest common factor of 512,400, we have to find the factors of both numbers and list the highest common factor.

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The HCF of 512,400 is 16.

Lets's calculate GCF of 512,400

Greatest Common Factor (GCF) of 512,400 By Common Division

2	512, 400
2	256, 200
2	128, 100
2	64, 50
	32, 25

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 512,400 By Matching Biggest Common Factor Method

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Now, list down the factors of 400

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Greatest Common Factor

We found the factors 512,400 . The biggest common factor number is the GCF number.
So the greatest common factor 512,400 is 16.

Lets's calculate LCM of 338,131

Lowest Common Multiple of 338,131 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 44278

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/44278

Therefore, the GCF of Fractions 512/338,400/131 is 16/44278

Least Common Multiple of 338,131 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 338,131 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(338,131) = 1

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

GCF(338,131) x common factors =1 x 1 = 1

LCM(338,131) = ( 338 × 131 ) / 1

LCM(338,131) = 44278 / 1

LCM(338,131) = 44278

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FAQs on GCF of Fractions of 512/338, 400/131

1. What is the HCF of 512,400?

The HCF of 512,400 is 16

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 512/338, 400/131?

Answer: GCF of Numerators as per given numbers 512/338, 400/131 is

GCF of Numerators i.e. for 512,400 is 16

LCM of denominators i.e. for 338,131 is 44278.

Thus, GCF of Fractions is 16/44278.Finally, GCF of Fractions for 512/338, 400/131 is 16/44278.