How to Find GCF of 2748/514, 3616/5686?

GCF of 2748/514, 3616/5686

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 2748/514, 3616/5686 i.e 4/1461302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2748/514, 3616/5686.

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 2748/514,3616/5686?

Given fractions are 2748/514,3616/5686

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 2748/514,3616/5686, numerators are 2748,3616

Denominators are 514,5686

The GCF of 2748,3616 is 4 .

LCM of 514,5686 is 1461302.

The greatest common factor of 2748/514,3616/5686 = [GCF of 2748,3616]/[LCM of 514,5686]= 4/1461302

Therefore, the GCF of 2748/514,3616/5686 is 4/1461302.

Greatest Common Factor of 2748,3616

To find the highest common factor of 2748,3616, we have to find the factors of both numbers and list the highest common factor.

The factors of 2748 are 1, 2, 3, 4, 6, 12, 229, 458, 687, 916, 1374, 2748

The factors of 3616 are 1, 2, 4, 8, 16, 32, 113, 226, 452, 904, 1808, 3616

The HCF of 2748,3616 is 4.

Lets's calculate GCF of 2748,3616

Greatest Common Factor (GCF) of 2748,3616 By Common Division

2	2748, 3616
2	1374, 1808
	687, 904

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 2748,3616 By Matching Biggest Common Factor Method

Now, list down the factors of 2748

1,2,3,4,6,12,229,458,687,916,1374,2748

Now, list down the factors of 3616

1,2,4,8,16,32,113,226,452,904,1808,3616

Greatest Common Factor

We found the factors 2748,3616 . The biggest common factor number is the GCF number.
So the greatest common factor 2748,3616 is 4.

Lets's calculate LCM of 514,5686

Lowest Common Multiple of 514,5686 using Common Division

2	514, 5686
	257, 2843

∴ So the LCM of the given numbers is 2 x 257 x 2843 = 1461302

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1461302

Therefore, the GCF of Fractions 2748/514,3616/5686 is 4/1461302

Least Common Multiple of 514,5686 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 514,5686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(514,5686) = 2

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

GCF(514,5686) x common factors =2 x 1 = 2

LCM(514,5686) = ( 514 × 5686 ) / 2

LCM(514,5686) = 2922604 / 2

LCM(514,5686) = 1461302

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FAQs on GCF of Fractions of 2748/514, 3616/5686

1. What is the HCF of 2748,3616?

The HCF of 2748,3616 is 4

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 2748/514, 3616/5686?

Answer: GCF of Numerators as per given numbers 2748/514, 3616/5686 is

GCF of Numerators i.e. for 2748,3616 is 4

LCM of denominators i.e. for 514,5686 is 1461302.

Thus, GCF of Fractions is 4/1461302.Finally, GCF of Fractions for 2748/514, 3616/5686 is 4/1461302.