How to Find GCF of 57/42, 37/90, 78/292?

GCF of 57/42, 37/90, 78/292

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 57/42, 37/90, 78/292 i.e 1/91980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 57/42, 37/90, 78/292.

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 57/42,37/90,78/292?

Given fractions are 57/42,37/90,78/292

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 57/42,37/90,78/292, numerators are 57,37,78

Denominators are 42,90,292

The GCF of 57,37,78 is 1 .

LCM of 42,90,292 is 91980.

The greatest common factor of 57/42,37/90,78/292 = [GCF of 57,37,78]/[LCM of 42,90,292]= 1/91980

Therefore, the GCF of 57/42,37/90,78/292 is 1/91980.

Greatest Common Factor of 57,37,78

To find the highest common factor of 57,37,78, 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 37 are 1, 37

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The HCF of 57,37,78 is 1.

Lets's calculate GCF of 57,37,78

Greatest Common Factor (GCF) of 57,37,78 By Common Division

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

Greatest Common Factor of 57,37,78 By Matching Biggest Common Factor Method

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 37

1,37

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Greatest Common Factor

We found the factors 57,37,78 . The biggest common factor number is the GCF number.
So the greatest common factor 57,37,78 is 1.

Lets's calculate LCM of 42,90,292

Lowest Common Multiple of 42,90,292 using Common Division

2	42, 90, 292
3	21, 45, 146
	7, 15, 146

∴ So the LCM of the given numbers is 2 x 3 x 7 x 15 x 146 = 91980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/91980

Therefore, the GCF of Fractions 57/42,37/90,78/292 is 1/91980

Least Common Multiple of 42,90,292 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 42,90,292 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,90,292) = 2

common factors(in case of two or more numbers have common factors) = 6

GCF(42,90,292) x common factors =2 x 6 = 12

LCM(42,90,292) = ( 42 × 90 × 292 ) / 12

LCM(42,90,292) = 1103760 / 12

LCM(42,90,292) = 91980

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FAQs on GCF of Fractions of 57/42, 37/90, 78/292

1. What is the HCF of 57,37,78?

The HCF of 57,37,78 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 57/42, 37/90, 78/292?

Answer: GCF of Numerators as per given numbers 57/42, 37/90, 78/292 is

GCF of Numerators i.e. for 57,37,78 is 1

LCM of denominators i.e. for 42,90,292 is 91980.

Thus, GCF of Fractions is 1/91980.Finally, GCF of Fractions for 57/42, 37/90, 78/292 is 1/91980.