How to Find GCF of 57/212, 90/656, 193/975?

GCF of 57/212, 90/656, 193/975

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 57/212, 90/656, 193/975 i.e 1/33898800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 57/212, 90/656, 193/975.

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 57/212,90/656,193/975?

Given fractions are 57/212,90/656,193/975

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 57/212,90/656,193/975, numerators are 57,90,193

Denominators are 212,656,975

The GCF of 57,90,193 is 1 .

LCM of 212,656,975 is 33898800.

The greatest common factor of 57/212,90/656,193/975 = [GCF of 57,90,193]/[LCM of 212,656,975]= 1/33898800

Therefore, the GCF of 57/212,90/656,193/975 is 1/33898800.

Greatest Common Factor of 57,90,193

To find the highest common factor of 57,90,193, we have to find the factors of both numbers and list the highest common factor.

The factors of 57 are 1, 3, 19, 57

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The factors of 193 are 1, 193

The HCF of 57,90,193 is 1.

Lets's calculate GCF of 57,90,193

Greatest Common Factor (GCF) of 57,90,193 By Common Division

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

Greatest Common Factor of 57,90,193 By Matching Biggest Common Factor Method

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 90

1,2,3,5,6,9,10,15,18,30,45,90

Now, list down the factors of 193

1,193

Greatest Common Factor

We found the factors 57,90,193 . The biggest common factor number is the GCF number.
So the greatest common factor 57,90,193 is 1.

Lets's calculate LCM of 212,656,975

Lowest Common Multiple of 212,656,975 using Common Division

2	212, 656, 975
2	106, 328, 975
	53, 164, 975

∴ So the LCM of the given numbers is 2 x 2 x 53 x 164 x 975 = 33898800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33898800

Therefore, the GCF of Fractions 57/212,90/656,193/975 is 1/33898800

Least Common Multiple of 212,656,975 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 212,656,975 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(212,656,975) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(212,656,975) x common factors =1 x 4 = 4

LCM(212,656,975) = ( 212 × 656 × 975 ) / 4

LCM(212,656,975) = 135595200 / 4

LCM(212,656,975) = 33898800

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FAQs on GCF of Fractions of 57/212, 90/656, 193/975

1. What is the HCF of 57,90,193?

The HCF of 57,90,193 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 57/212, 90/656, 193/975?

Answer: GCF of Numerators as per given numbers 57/212, 90/656, 193/975 is

GCF of Numerators i.e. for 57,90,193 is 1

LCM of denominators i.e. for 212,656,975 is 33898800.

Thus, GCF of Fractions is 1/33898800.Finally, GCF of Fractions for 57/212, 90/656, 193/975 is 1/33898800.