How to Find GCF of 92/30, 37/39, 278/444?

GCF of 92/30, 37/39, 278/444

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 92/30, 37/39, 278/444 i.e 1/28860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 92/30, 37/39, 278/444.

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 92/30,37/39,278/444?

Given fractions are 92/30,37/39,278/444

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 92/30,37/39,278/444, numerators are 92,37,278

Denominators are 30,39,444

The GCF of 92,37,278 is 1 .

LCM of 30,39,444 is 28860.

The greatest common factor of 92/30,37/39,278/444 = [GCF of 92,37,278]/[LCM of 30,39,444]= 1/28860

Therefore, the GCF of 92/30,37/39,278/444 is 1/28860.

Greatest Common Factor of 92,37,278

To find the highest common factor of 92,37,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 92 are 1, 2, 4, 23, 46, 92

The factors of 37 are 1, 37

The factors of 278 are 1, 2, 139, 278

The HCF of 92,37,278 is 1.

Lets's calculate GCF of 92,37,278

Greatest Common Factor (GCF) of 92,37,278 By Common Division

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

Greatest Common Factor of 92,37,278 By Matching Biggest Common Factor Method

Now, list down the factors of 92

1,2,4,23,46,92

Now, list down the factors of 37

1,37

Now, list down the factors of 278

1,2,139,278

Greatest Common Factor

We found the factors 92,37,278 . The biggest common factor number is the GCF number.
So the greatest common factor 92,37,278 is 1.

Lets's calculate LCM of 30,39,444

Lowest Common Multiple of 30,39,444 using Common Division

2	30, 39, 444
3	15, 39, 222
	5, 13, 74

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 74 = 28860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28860

Therefore, the GCF of Fractions 92/30,37/39,278/444 is 1/28860

Least Common Multiple of 30,39,444 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 30,39,444 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,39,444) = 3

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

GCF(30,39,444) x common factors =3 x 6 = 18

LCM(30,39,444) = ( 30 × 39 × 444 ) / 18

LCM(30,39,444) = 519480 / 18

LCM(30,39,444) = 28860

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FAQs on GCF of Fractions of 92/30, 37/39, 278/444

1. What is the HCF of 92,37,278?

The HCF of 92,37,278 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 92/30, 37/39, 278/444?

Answer: GCF of Numerators as per given numbers 92/30, 37/39, 278/444 is

GCF of Numerators i.e. for 92,37,278 is 1

LCM of denominators i.e. for 30,39,444 is 28860.

Thus, GCF of Fractions is 1/28860.Finally, GCF of Fractions for 92/30, 37/39, 278/444 is 1/28860.