How to Find GCF of 32/27, 53/90, 208/112?

GCF of 32/27, 53/90, 208/112

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 32/27, 53/90, 208/112 i.e 1/15120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/27, 53/90, 208/112.

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 32/27,53/90,208/112?

Given fractions are 32/27,53/90,208/112

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 32/27,53/90,208/112, numerators are 32,53,208

Denominators are 27,90,112

The GCF of 32,53,208 is 1 .

LCM of 27,90,112 is 15120.

The greatest common factor of 32/27,53/90,208/112 = [GCF of 32,53,208]/[LCM of 27,90,112]= 1/15120

Therefore, the GCF of 32/27,53/90,208/112 is 1/15120.

Greatest Common Factor of 32,53,208

To find the highest common factor of 32,53,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 32 are 1, 2, 4, 8, 16, 32

The factors of 53 are 1, 53

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 32,53,208 is 1.

Lets's calculate GCF of 32,53,208

Greatest Common Factor (GCF) of 32,53,208 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 32,53,208 By Matching Biggest Common Factor Method

Now, list down the factors of 32

1,2,4,8,16,32

Now, list down the factors of 53

1,53

Now, list down the factors of 208

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 32,53,208 . The biggest common factor number is the GCF number.
So the greatest common factor 32,53,208 is 1.

Lets's calculate LCM of 27,90,112

Lowest Common Multiple of 27,90,112 using Common Division

2	27, 90, 112
3	27, 45, 56
3	9, 15, 56
	3, 5, 56

∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 56 = 15120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15120

Therefore, the GCF of Fractions 32/27,53/90,208/112 is 1/15120

Least Common Multiple of 27,90,112 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 27,90,112 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,90,112) = 1

common factors(in case of two or more numbers have common factors) = 18

GCF(27,90,112) x common factors =1 x 18 = 18

LCM(27,90,112) = ( 27 × 90 × 112 ) / 18

LCM(27,90,112) = 272160 / 18

LCM(27,90,112) = 15120

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 32/27, 53/90, 208/112

1. What is the HCF of 32,53,208?

The HCF of 32,53,208 is 1

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 32/27, 53/90, 208/112?

Answer: GCF of Numerators as per given numbers 32/27, 53/90, 208/112 is

GCF of Numerators i.e. for 32,53,208 is 1

LCM of denominators i.e. for 27,90,112 is 15120.

Thus, GCF of Fractions is 1/15120.Finally, GCF of Fractions for 32/27, 53/90, 208/112 is 1/15120.