How to Find GCF of 242/304, 506/331?

GCF of 242/304, 506/331

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 242/304, 506/331 i.e 22/100624 easily. The following is the detailed procedure to determine the greatest common factor of fractions 242/304, 506/331.

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 242/304,506/331?

Given fractions are 242/304,506/331

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 242/304,506/331, numerators are 242,506

Denominators are 304,331

The GCF of 242,506 is 22 .

LCM of 304,331 is 100624.

The greatest common factor of 242/304,506/331 = [GCF of 242,506]/[LCM of 304,331]= 22/100624

Therefore, the GCF of 242/304,506/331 is 22/100624.

Greatest Common Factor of 242,506

To find the highest common factor of 242,506, we have to find the factors of both numbers and list the highest common factor.

The factors of 242 are 1, 2, 11, 22, 121, 242

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 242,506 is 22.

Lets's calculate GCF of 242,506

Greatest Common Factor (GCF) of 242,506 By Common Division

2	242, 506
11	121, 253
	11, 23

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 242,506 By Matching Biggest Common Factor Method

Now, list down the factors of 242

1,2,11,22,121,242

Now, list down the factors of 506

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 242,506 . The biggest common factor number is the GCF number.
So the greatest common factor 242,506 is 22.

Lets's calculate LCM of 304,331

Lowest Common Multiple of 304,331 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 100624

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/100624

Therefore, the GCF of Fractions 242/304,506/331 is 22/100624

Least Common Multiple of 304,331 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 304,331 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(304,331) = 1

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

GCF(304,331) x common factors =1 x 1 = 1

LCM(304,331) = ( 304 × 331 ) / 1

LCM(304,331) = 100624 / 1

LCM(304,331) = 100624

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FAQs on GCF of Fractions of 242/304, 506/331

1. What is the HCF of 242,506?

The HCF of 242,506 is 22

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 242/304, 506/331?

Answer: GCF of Numerators as per given numbers 242/304, 506/331 is

GCF of Numerators i.e. for 242,506 is 22

LCM of denominators i.e. for 304,331 is 100624.

Thus, GCF of Fractions is 22/100624.Finally, GCF of Fractions for 242/304, 506/331 is 22/100624.