How to Find GCF of 112/53, 200/738?

GCF of 112/53, 200/738

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 112/53, 200/738 i.e 8/39114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/53, 200/738.

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 112/53,200/738?

Given fractions are 112/53,200/738

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 112/53,200/738, numerators are 112,200

Denominators are 53,738

The GCF of 112,200 is 8 .

LCM of 53,738 is 39114.

The greatest common factor of 112/53,200/738 = [GCF of 112,200]/[LCM of 53,738]= 8/39114

Therefore, the GCF of 112/53,200/738 is 8/39114.

Greatest Common Factor of 112,200

To find the highest common factor of 112,200, we have to find the factors of both numbers and list the highest common factor.

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

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

The HCF of 112,200 is 8.

Lets's calculate GCF of 112,200

Greatest Common Factor (GCF) of 112,200 By Common Division

2	112, 200
2	56, 100
2	28, 50
	14, 25

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

Greatest Common Factor of 112,200 By Matching Biggest Common Factor Method

Now, list down the factors of 112

1,2,4,7,8,14,16,28,56,112

Now, list down the factors of 200

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

Greatest Common Factor

We found the factors 112,200 . The biggest common factor number is the GCF number.
So the greatest common factor 112,200 is 8.

Lets's calculate LCM of 53,738

Lowest Common Multiple of 53,738 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 39114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/39114

Therefore, the GCF of Fractions 112/53,200/738 is 8/39114

Least Common Multiple of 53,738 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 53,738 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(53,738) = 1

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

GCF(53,738) x common factors =1 x 1 = 1

LCM(53,738) = ( 53 × 738 ) / 1

LCM(53,738) = 39114 / 1

LCM(53,738) = 39114

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FAQs on GCF of Fractions of 112/53, 200/738

1. What is the HCF of 112,200?

The HCF of 112,200 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 112/53, 200/738?

Answer: GCF of Numerators as per given numbers 112/53, 200/738 is

GCF of Numerators i.e. for 112,200 is 8

LCM of denominators i.e. for 53,738 is 39114.

Thus, GCF of Fractions is 8/39114.Finally, GCF of Fractions for 112/53, 200/738 is 8/39114.