How to Find GCF of 660/272, 561/320?

GCF of 660/272, 561/320

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 660/272, 561/320 i.e 33/5440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/272, 561/320.

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 660/272,561/320?

Given fractions are 660/272,561/320

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 660/272,561/320, numerators are 660,561

Denominators are 272,320

The GCF of 660,561 is 33 .

LCM of 272,320 is 5440.

The greatest common factor of 660/272,561/320 = [GCF of 660,561]/[LCM of 272,320]= 33/5440

Therefore, the GCF of 660/272,561/320 is 33/5440.

Greatest Common Factor of 660,561

To find the highest common factor of 660,561, we have to find the factors of both numbers and list the highest common factor.

The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660

The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561

The HCF of 660,561 is 33.

Lets's calculate GCF of 660,561

Greatest Common Factor (GCF) of 660,561 By Common Division

3	660, 561
11	220, 187
	20, 17

∴ So the GCF of the given numbers is 3 x 11 = 33

Greatest Common Factor of 660,561 By Matching Biggest Common Factor Method

Now, list down the factors of 660

1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660

Now, list down the factors of 561

1,3,11,17,33,51,187,561

Greatest Common Factor

We found the factors 660,561 . The biggest common factor number is the GCF number.
So the greatest common factor 660,561 is 33.

Lets's calculate LCM of 272,320

Lowest Common Multiple of 272,320 using Common Division

2	272, 320
2	136, 160
2	68, 80
2	34, 40
	17, 20

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 17 x 20 = 5440

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/5440

Therefore, the GCF of Fractions 660/272,561/320 is 33/5440

Least Common Multiple of 272,320 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 272,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(272,320) = 16

common factors(in case of two or more numbers have common factors) = 1

GCF(272,320) x common factors =16 x 1 = 16

LCM(272,320) = ( 272 × 320 ) / 16

LCM(272,320) = 87040 / 16

LCM(272,320) = 5440

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FAQs on GCF of Fractions of 660/272, 561/320

1. What is the HCF of 660,561?

The HCF of 660,561 is 33

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 660/272, 561/320?

Answer: GCF of Numerators as per given numbers 660/272, 561/320 is

GCF of Numerators i.e. for 660,561 is 33

LCM of denominators i.e. for 272,320 is 5440.

Thus, GCF of Fractions is 33/5440.Finally, GCF of Fractions for 660/272, 561/320 is 33/5440.