How to Find GCF of 5728/260, 7078/4784?

GCF of 5728/260, 7078/4784

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 5728/260, 7078/4784 i.e 2/23920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5728/260, 7078/4784.

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 5728/260,7078/4784?

Given fractions are 5728/260,7078/4784

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 5728/260,7078/4784, numerators are 5728,7078

Denominators are 260,4784

The GCF of 5728,7078 is 2 .

LCM of 260,4784 is 23920.

The greatest common factor of 5728/260,7078/4784 = [GCF of 5728,7078]/[LCM of 260,4784]= 2/23920

Therefore, the GCF of 5728/260,7078/4784 is 2/23920.

Greatest Common Factor of 5728,7078

To find the highest common factor of 5728,7078, we have to find the factors of both numbers and list the highest common factor.

The factors of 5728 are 1, 2, 4, 8, 16, 32, 179, 358, 716, 1432, 2864, 5728

The factors of 7078 are 1, 2, 3539, 7078

The HCF of 5728,7078 is 2.

Lets's calculate GCF of 5728,7078

Greatest Common Factor (GCF) of 5728,7078 By Common Division

2	5728, 7078
	2864, 3539

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

Greatest Common Factor of 5728,7078 By Matching Biggest Common Factor Method

Now, list down the factors of 5728

1,2,4,8,16,32,179,358,716,1432,2864,5728

Now, list down the factors of 7078

1,2,3539,7078

Greatest Common Factor

We found the factors 5728,7078 . The biggest common factor number is the GCF number.
So the greatest common factor 5728,7078 is 2.

Lets's calculate LCM of 260,4784

Lowest Common Multiple of 260,4784 using Common Division

2	260, 4784
2	130, 2392
13	65, 1196
	5, 92

∴ So the LCM of the given numbers is 2 x 2 x 13 x 5 x 92 = 23920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/23920

Therefore, the GCF of Fractions 5728/260,7078/4784 is 2/23920

Least Common Multiple of 260,4784 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 260,4784 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(260,4784) = 52

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

GCF(260,4784) x common factors =52 x 1 = 52

LCM(260,4784) = ( 260 × 4784 ) / 52

LCM(260,4784) = 1243840 / 52

LCM(260,4784) = 23920

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FAQs on GCF of Fractions of 5728/260, 7078/4784

1. What is the HCF of 5728,7078?

The HCF of 5728,7078 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 5728/260, 7078/4784?

Answer: GCF of Numerators as per given numbers 5728/260, 7078/4784 is

GCF of Numerators i.e. for 5728,7078 is 2

LCM of denominators i.e. for 260,4784 is 23920.

Thus, GCF of Fractions is 2/23920.Finally, GCF of Fractions for 5728/260, 7078/4784 is 2/23920.