How to Find GCF of 200/38, 512/1092?

GCF of 200/38, 512/1092

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 200/38, 512/1092 i.e 8/20748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 200/38, 512/1092.

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 200/38,512/1092?

Given fractions are 200/38,512/1092

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 200/38,512/1092, numerators are 200,512

Denominators are 38,1092

The GCF of 200,512 is 8 .

LCM of 38,1092 is 20748.

The greatest common factor of 200/38,512/1092 = [GCF of 200,512]/[LCM of 38,1092]= 8/20748

Therefore, the GCF of 200/38,512/1092 is 8/20748.

Greatest Common Factor of 200,512

To find the highest common factor of 200,512, we have to find the factors of both numbers and list the highest common factor.

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

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

The HCF of 200,512 is 8.

Lets's calculate GCF of 200,512

Greatest Common Factor (GCF) of 200,512 By Common Division

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

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 200,512 By Matching Biggest Common Factor Method

Now, list down the factors of 200

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

Now, list down the factors of 512

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

Greatest Common Factor

We found the factors 200,512 . The biggest common factor number is the GCF number.
So the greatest common factor 200,512 is 8.

Lets's calculate LCM of 38,1092

Lowest Common Multiple of 38,1092 using Common Division

2	38, 1092
	19, 546

∴ So the LCM of the given numbers is 2 x 19 x 546 = 20748

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/20748

Therefore, the GCF of Fractions 200/38,512/1092 is 8/20748

Least Common Multiple of 38,1092 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 38,1092 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,1092) = 2

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

GCF(38,1092) x common factors =2 x 1 = 2

LCM(38,1092) = ( 38 × 1092 ) / 2

LCM(38,1092) = 41496 / 2

LCM(38,1092) = 20748

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FAQs on GCF of Fractions of 200/38, 512/1092

1. What is the HCF of 200,512?

The HCF of 200,512 is 8

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 200/38, 512/1092?

Answer: GCF of Numerators as per given numbers 200/38, 512/1092 is

GCF of Numerators i.e. for 200,512 is 8

LCM of denominators i.e. for 38,1092 is 20748.

Thus, GCF of Fractions is 8/20748.Finally, GCF of Fractions for 200/38, 512/1092 is 8/20748.