How to Find GCF of 2737/274, 7521/206?

GCF of 2737/274, 7521/206

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 2737/274, 7521/206 i.e 23/28222 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2737/274, 7521/206.

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 2737/274,7521/206?

Given fractions are 2737/274,7521/206

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 2737/274,7521/206, numerators are 2737,7521

Denominators are 274,206

The GCF of 2737,7521 is 23 .

LCM of 274,206 is 28222.

The greatest common factor of 2737/274,7521/206 = [GCF of 2737,7521]/[LCM of 274,206]= 23/28222

Therefore, the GCF of 2737/274,7521/206 is 23/28222.

Greatest Common Factor of 2737,7521

To find the highest common factor of 2737,7521, we have to find the factors of both numbers and list the highest common factor.

The factors of 2737 are 1, 7, 17, 23, 119, 161, 391, 2737

The factors of 7521 are 1, 3, 23, 69, 109, 327, 2507, 7521

The HCF of 2737,7521 is 23.

Lets's calculate GCF of 2737,7521

Greatest Common Factor (GCF) of 2737,7521 By Common Division

23	2737, 7521
	119, 327

∴ So the GCF of the given numbers is 23 = 23

Greatest Common Factor of 2737,7521 By Matching Biggest Common Factor Method

Now, list down the factors of 2737

1,7,17,23,119,161,391,2737

Now, list down the factors of 7521

1,3,23,69,109,327,2507,7521

Greatest Common Factor

We found the factors 2737,7521 . The biggest common factor number is the GCF number.
So the greatest common factor 2737,7521 is 23.

Lets's calculate LCM of 274,206

Lowest Common Multiple of 274,206 using Common Division

2	274, 206
	137, 103

∴ So the LCM of the given numbers is 2 x 137 x 103 = 28222

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/28222

Therefore, the GCF of Fractions 2737/274,7521/206 is 23/28222

Least Common Multiple of 274,206 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 274,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,206) = 2

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

GCF(274,206) x common factors =2 x 1 = 2

LCM(274,206) = ( 274 × 206 ) / 2

LCM(274,206) = 56444 / 2

LCM(274,206) = 28222

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FAQs on GCF of Fractions of 2737/274, 7521/206

1. What is the HCF of 2737,7521?

The HCF of 2737,7521 is 23

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 2737/274, 7521/206?

Answer: GCF of Numerators as per given numbers 2737/274, 7521/206 is

GCF of Numerators i.e. for 2737,7521 is 23

LCM of denominators i.e. for 274,206 is 28222.

Thus, GCF of Fractions is 23/28222.Finally, GCF of Fractions for 2737/274, 7521/206 is 23/28222.