How to Find GCF of 74/296, 28/736, 390/684?

GCF of 74/296, 28/736, 390/684

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 74/296, 28/736, 390/684 i.e 2/4656672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/296, 28/736, 390/684.

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 74/296,28/736,390/684?

Given fractions are 74/296,28/736,390/684

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 74/296,28/736,390/684, numerators are 74,28,390

Denominators are 296,736,684

The GCF of 74,28,390 is 2 .

LCM of 296,736,684 is 4656672.

The greatest common factor of 74/296,28/736,390/684 = [GCF of 74,28,390]/[LCM of 296,736,684]= 2/4656672

Therefore, the GCF of 74/296,28/736,390/684 is 2/4656672.

Greatest Common Factor of 74,28,390

To find the highest common factor of 74,28,390, we have to find the factors of both numbers and list the highest common factor.

The factors of 74 are 1, 2, 37, 74

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

The HCF of 74,28,390 is 2.

Lets's calculate GCF of 74,28,390

Greatest Common Factor (GCF) of 74,28,390 By Common Division

2	74, 28, 390
	37, 14, 195

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

Greatest Common Factor of 74,28,390 By Matching Biggest Common Factor Method

Now, list down the factors of 74

1,2,37,74

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 390

1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390

Greatest Common Factor

We found the factors 74,28,390 . The biggest common factor number is the GCF number.
So the greatest common factor 74,28,390 is 2.

Lets's calculate LCM of 296,736,684

Lowest Common Multiple of 296,736,684 using Common Division

2	296, 736, 684
2	148, 368, 342
2	74, 184, 171
	37, 92, 171

∴ So the LCM of the given numbers is 2 x 2 x 2 x 37 x 92 x 171 = 4656672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4656672

Therefore, the GCF of Fractions 74/296,28/736,390/684 is 2/4656672

Least Common Multiple of 296,736,684 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 296,736,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(296,736,684) = 4

common factors(in case of two or more numbers have common factors) = 8

GCF(296,736,684) x common factors =4 x 8 = 32

LCM(296,736,684) = ( 296 × 736 × 684 ) / 32

LCM(296,736,684) = 149013504 / 32

LCM(296,736,684) = 4656672

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 74/296, 28/736, 390/684

1. What is the HCF of 74,28,390?

The HCF of 74,28,390 is 2

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 74/296, 28/736, 390/684?

Answer: GCF of Numerators as per given numbers 74/296, 28/736, 390/684 is

GCF of Numerators i.e. for 74,28,390 is 2

LCM of denominators i.e. for 296,736,684 is 4656672.

Thus, GCF of Fractions is 2/4656672.Finally, GCF of Fractions for 74/296, 28/736, 390/684 is 2/4656672.