How to Find GCF of 2704/293, 3614/3672?

GCF of 2704/293, 3614/3672

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 2704/293, 3614/3672 i.e 26/1075896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2704/293, 3614/3672.

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 2704/293,3614/3672?

Given fractions are 2704/293,3614/3672

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 2704/293,3614/3672, numerators are 2704,3614

Denominators are 293,3672

The GCF of 2704,3614 is 26 .

LCM of 293,3672 is 1075896.

The greatest common factor of 2704/293,3614/3672 = [GCF of 2704,3614]/[LCM of 293,3672]= 26/1075896

Therefore, the GCF of 2704/293,3614/3672 is 26/1075896.

Greatest Common Factor of 2704,3614

To find the highest common factor of 2704,3614, we have to find the factors of both numbers and list the highest common factor.

The factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704

The factors of 3614 are 1, 2, 13, 26, 139, 278, 1807, 3614

The HCF of 2704,3614 is 26.

Lets's calculate GCF of 2704,3614

Greatest Common Factor (GCF) of 2704,3614 By Common Division

2	2704, 3614
13	1352, 1807
	104, 139

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 2704,3614 By Matching Biggest Common Factor Method

Now, list down the factors of 2704

1,2,4,8,13,16,26,52,104,169,208,338,676,1352,2704

Now, list down the factors of 3614

1,2,13,26,139,278,1807,3614

Greatest Common Factor

We found the factors 2704,3614 . The biggest common factor number is the GCF number.
So the greatest common factor 2704,3614 is 26.

Lets's calculate LCM of 293,3672

Lowest Common Multiple of 293,3672 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1075896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/1075896

Therefore, the GCF of Fractions 2704/293,3614/3672 is 26/1075896

Least Common Multiple of 293,3672 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 293,3672 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(293,3672) = 1

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

GCF(293,3672) x common factors =1 x 1 = 1

LCM(293,3672) = ( 293 × 3672 ) / 1

LCM(293,3672) = 1075896 / 1

LCM(293,3672) = 1075896

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FAQs on GCF of Fractions of 2704/293, 3614/3672

1. What is the HCF of 2704,3614?

The HCF of 2704,3614 is 26

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 2704/293, 3614/3672?

Answer: GCF of Numerators as per given numbers 2704/293, 3614/3672 is

GCF of Numerators i.e. for 2704,3614 is 26

LCM of denominators i.e. for 293,3672 is 1075896.

Thus, GCF of Fractions is 26/1075896.Finally, GCF of Fractions for 2704/293, 3614/3672 is 26/1075896.