How to Find GCF of 560/580, 440/270?

GCF of 560/580, 440/270

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 560/580, 440/270 i.e 40/15660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/580, 440/270.

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 560/580,440/270?

Given fractions are 560/580,440/270

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 560/580,440/270, numerators are 560,440

Denominators are 580,270

The GCF of 560,440 is 40 .

LCM of 580,270 is 15660.

The greatest common factor of 560/580,440/270 = [GCF of 560,440]/[LCM of 580,270]= 40/15660

Therefore, the GCF of 560/580,440/270 is 40/15660.

Greatest Common Factor of 560,440

To find the highest common factor of 560,440, we have to find the factors of both numbers and list the highest common factor.

The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440

The HCF of 560,440 is 40.

Lets's calculate GCF of 560,440

Greatest Common Factor (GCF) of 560,440 By Common Division

2	560, 440
2	280, 220
2	140, 110
5	70, 55
	14, 11

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 560,440 By Matching Biggest Common Factor Method

Now, list down the factors of 560

1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560

Now, list down the factors of 440

1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440

Greatest Common Factor

We found the factors 560,440 . The biggest common factor number is the GCF number.
So the greatest common factor 560,440 is 40.

Lets's calculate LCM of 580,270

Lowest Common Multiple of 580,270 using Common Division

2	580, 270
5	290, 135
	58, 27

∴ So the LCM of the given numbers is 2 x 5 x 58 x 27 = 15660

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/15660

Therefore, the GCF of Fractions 560/580,440/270 is 40/15660

Least Common Multiple of 580,270 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 580,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(580,270) = 10

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

GCF(580,270) x common factors =10 x 1 = 10

LCM(580,270) = ( 580 × 270 ) / 10

LCM(580,270) = 156600 / 10

LCM(580,270) = 15660

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FAQs on GCF of Fractions of 560/580, 440/270

1. What is the HCF of 560,440?

The HCF of 560,440 is 40

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 560/580, 440/270?

Answer: GCF of Numerators as per given numbers 560/580, 440/270 is

GCF of Numerators i.e. for 560,440 is 40

LCM of denominators i.e. for 580,270 is 15660.

Thus, GCF of Fractions is 40/15660.Finally, GCF of Fractions for 560/580, 440/270 is 40/15660.