How to Find GCF of 520/270, 8768/284?

GCF of 520/270, 8768/284

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 520/270, 8768/284 i.e 8/38340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/270, 8768/284.

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 520/270,8768/284?

Given fractions are 520/270,8768/284

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 520/270,8768/284, numerators are 520,8768

Denominators are 270,284

The GCF of 520,8768 is 8 .

LCM of 270,284 is 38340.

The greatest common factor of 520/270,8768/284 = [GCF of 520,8768]/[LCM of 270,284]= 8/38340

Therefore, the GCF of 520/270,8768/284 is 8/38340.

Greatest Common Factor of 520,8768

To find the highest common factor of 520,8768, we have to find the factors of both numbers and list the highest common factor.

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

The factors of 8768 are 1, 2, 4, 8, 16, 32, 64, 137, 274, 548, 1096, 2192, 4384, 8768

The HCF of 520,8768 is 8.

Lets's calculate GCF of 520,8768

Greatest Common Factor (GCF) of 520,8768 By Common Division

2	520, 8768
2	260, 4384
2	130, 2192
	65, 1096

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 520,8768 By Matching Biggest Common Factor Method

Now, list down the factors of 520

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Now, list down the factors of 8768

1,2,4,8,16,32,64,137,274,548,1096,2192,4384,8768

Greatest Common Factor

We found the factors 520,8768 . The biggest common factor number is the GCF number.
So the greatest common factor 520,8768 is 8.

Lets's calculate LCM of 270,284

Lowest Common Multiple of 270,284 using Common Division

2	270, 284
	135, 142

∴ So the LCM of the given numbers is 2 x 135 x 142 = 38340

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/38340

Therefore, the GCF of Fractions 520/270,8768/284 is 8/38340

Least Common Multiple of 270,284 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 270,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(270,284) = 2

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

GCF(270,284) x common factors =2 x 1 = 2

LCM(270,284) = ( 270 × 284 ) / 2

LCM(270,284) = 76680 / 2

LCM(270,284) = 38340

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FAQs on GCF of Fractions of 520/270, 8768/284

1. What is the HCF of 520,8768?

The HCF of 520,8768 is 8

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 520/270, 8768/284?

Answer: GCF of Numerators as per given numbers 520/270, 8768/284 is

GCF of Numerators i.e. for 520,8768 is 8

LCM of denominators i.e. for 270,284 is 38340.

Thus, GCF of Fractions is 8/38340.Finally, GCF of Fractions for 520/270, 8768/284 is 8/38340.