How to Find GCF of 28/31, 738/32, 223/566?

GCF of 28/31, 738/32, 223/566

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 28/31, 738/32, 223/566 i.e 1/280736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/31, 738/32, 223/566.

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 28/31,738/32,223/566?

Given fractions are 28/31,738/32,223/566

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 28/31,738/32,223/566, numerators are 28,738,223

Denominators are 31,32,566

The GCF of 28,738,223 is 1 .

LCM of 31,32,566 is 280736.

The greatest common factor of 28/31,738/32,223/566 = [GCF of 28,738,223]/[LCM of 31,32,566]= 1/280736

Therefore, the GCF of 28/31,738/32,223/566 is 1/280736.

Greatest Common Factor of 28,738,223

To find the highest common factor of 28,738,223, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738

The factors of 223 are 1, 223

The HCF of 28,738,223 is 1.

Lets's calculate GCF of 28,738,223

Greatest Common Factor (GCF) of 28,738,223 By Common Division

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

Greatest Common Factor of 28,738,223 By Matching Biggest Common Factor Method

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 738

1,2,3,6,9,18,41,82,123,246,369,738

Now, list down the factors of 223

1,223

Greatest Common Factor

We found the factors 28,738,223 . The biggest common factor number is the GCF number.
So the greatest common factor 28,738,223 is 1.

Lets's calculate LCM of 31,32,566

Lowest Common Multiple of 31,32,566 using Common Division

2	31, 32, 566
	31, 16, 283

∴ So the LCM of the given numbers is 2 x 31 x 16 x 283 = 280736

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/280736

Therefore, the GCF of Fractions 28/31,738/32,223/566 is 1/280736

Least Common Multiple of 31,32,566 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 31,32,566 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,32,566) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(31,32,566) x common factors =1 x 2 = 2

LCM(31,32,566) = ( 31 × 32 × 566 ) / 2

LCM(31,32,566) = 561472 / 2

LCM(31,32,566) = 280736

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 28/31, 738/32, 223/566

1. What is the HCF of 28,738,223?

The HCF of 28,738,223 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 28/31, 738/32, 223/566?

Answer: GCF of Numerators as per given numbers 28/31, 738/32, 223/566 is

GCF of Numerators i.e. for 28,738,223 is 1

LCM of denominators i.e. for 31,32,566 is 280736.

Thus, GCF of Fractions is 1/280736.Finally, GCF of Fractions for 28/31, 738/32, 223/566 is 1/280736.