How to Find GCF of 307/490, 7238/180?

GCF of 307/490, 7238/180

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 307/490, 7238/180 i.e 1/8820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 307/490, 7238/180.

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 307/490,7238/180?

Given fractions are 307/490,7238/180

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 307/490,7238/180, numerators are 307,7238

Denominators are 490,180

The GCF of 307,7238 is 1 .

LCM of 490,180 is 8820.

The greatest common factor of 307/490,7238/180 = [GCF of 307,7238]/[LCM of 490,180]= 1/8820

Therefore, the GCF of 307/490,7238/180 is 1/8820.

Greatest Common Factor of 307,7238

To find the highest common factor of 307,7238, we have to find the factors of both numbers and list the highest common factor.

The factors of 307 are 1, 307

The factors of 7238 are 1, 2, 7, 11, 14, 22, 47, 77, 94, 154, 329, 517, 658, 1034, 3619, 7238

The HCF of 307,7238 is 1.

Lets's calculate GCF of 307,7238

Greatest Common Factor (GCF) of 307,7238 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 307,7238 By Matching Biggest Common Factor Method

Now, list down the factors of 307

1,307

Now, list down the factors of 7238

1,2,7,11,14,22,47,77,94,154,329,517,658,1034,3619,7238

Greatest Common Factor

We found the factors 307,7238 . The biggest common factor number is the GCF number.
So the greatest common factor 307,7238 is 1.

Lets's calculate LCM of 490,180

Lowest Common Multiple of 490,180 using Common Division

2	490, 180
5	245, 90
	49, 18

∴ So the LCM of the given numbers is 2 x 5 x 49 x 18 = 8820

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8820

Therefore, the GCF of Fractions 307/490,7238/180 is 1/8820

Least Common Multiple of 490,180 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 490,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(490,180) = 10

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

GCF(490,180) x common factors =10 x 1 = 10

LCM(490,180) = ( 490 × 180 ) / 10

LCM(490,180) = 88200 / 10

LCM(490,180) = 8820

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FAQs on GCF of Fractions of 307/490, 7238/180

1. What is the HCF of 307,7238?

The HCF of 307,7238 is 1

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 307/490, 7238/180?

Answer: GCF of Numerators as per given numbers 307/490, 7238/180 is

GCF of Numerators i.e. for 307,7238 is 1

LCM of denominators i.e. for 490,180 is 8820.

Thus, GCF of Fractions is 1/8820.Finally, GCF of Fractions for 307/490, 7238/180 is 1/8820.