How to Find GCF of 308/291, 420/940?

GCF of 308/291, 420/940

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 308/291, 420/940 i.e 28/273540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/291, 420/940.

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 308/291,420/940?

Given fractions are 308/291,420/940

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 308/291,420/940, numerators are 308,420

Denominators are 291,940

The GCF of 308,420 is 28 .

LCM of 291,940 is 273540.

The greatest common factor of 308/291,420/940 = [GCF of 308,420]/[LCM of 291,940]= 28/273540

Therefore, the GCF of 308/291,420/940 is 28/273540.

Greatest Common Factor of 308,420

To find the highest common factor of 308,420, we have to find the factors of both numbers and list the highest common factor.

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 308,420 is 28.

Lets's calculate GCF of 308,420

Greatest Common Factor (GCF) of 308,420 By Common Division

2	308, 420
2	154, 210
7	77, 105
	11, 15

∴ So the GCF of the given numbers is 2 x 2 x 7 = 28

Greatest Common Factor of 308,420 By Matching Biggest Common Factor Method

Now, list down the factors of 308

1,2,4,7,11,14,22,28,44,77,154,308

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 308,420 . The biggest common factor number is the GCF number.
So the greatest common factor 308,420 is 28.

Lets's calculate LCM of 291,940

Lowest Common Multiple of 291,940 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 273540

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/273540

Therefore, the GCF of Fractions 308/291,420/940 is 28/273540

Least Common Multiple of 291,940 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 291,940 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(291,940) = 1

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

GCF(291,940) x common factors =1 x 1 = 1

LCM(291,940) = ( 291 × 940 ) / 1

LCM(291,940) = 273540 / 1

LCM(291,940) = 273540

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FAQs on GCF of Fractions of 308/291, 420/940

1. What is the HCF of 308,420?

The HCF of 308,420 is 28

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 308/291, 420/940?

Answer: GCF of Numerators as per given numbers 308/291, 420/940 is

GCF of Numerators i.e. for 308,420 is 28

LCM of denominators i.e. for 291,940 is 273540.

Thus, GCF of Fractions is 28/273540.Finally, GCF of Fractions for 308/291, 420/940 is 28/273540.