How to Find GCF of 196/261, 480/978?

GCF of 196/261, 480/978

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 196/261, 480/978 i.e 4/85086 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/261, 480/978.

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 196/261,480/978?

Given fractions are 196/261,480/978

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 196/261,480/978, numerators are 196,480

Denominators are 261,978

The GCF of 196,480 is 4 .

LCM of 261,978 is 85086.

The greatest common factor of 196/261,480/978 = [GCF of 196,480]/[LCM of 261,978]= 4/85086

Therefore, the GCF of 196/261,480/978 is 4/85086.

Greatest Common Factor of 196,480

To find the highest common factor of 196,480, we have to find the factors of both numbers and list the highest common factor.

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

The HCF of 196,480 is 4.

Lets's calculate GCF of 196,480

Greatest Common Factor (GCF) of 196,480 By Common Division

2	196, 480
2	98, 240
	49, 120

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 196,480 By Matching Biggest Common Factor Method

Now, list down the factors of 196

1,2,4,7,14,28,49,98,196

Now, list down the factors of 480

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480

Greatest Common Factor

We found the factors 196,480 . The biggest common factor number is the GCF number.
So the greatest common factor 196,480 is 4.

Lets's calculate LCM of 261,978

Lowest Common Multiple of 261,978 using Common Division

3	261, 978
	87, 326

∴ So the LCM of the given numbers is 3 x 87 x 326 = 85086

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/85086

Therefore, the GCF of Fractions 196/261,480/978 is 4/85086

Least Common Multiple of 261,978 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 261,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(261,978) = 3

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

GCF(261,978) x common factors =3 x 1 = 3

LCM(261,978) = ( 261 × 978 ) / 3

LCM(261,978) = 255258 / 3

LCM(261,978) = 85086

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 196/261, 480/978

1. What is the HCF of 196,480?

The HCF of 196,480 is 4

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 196/261, 480/978?

Answer: GCF of Numerators as per given numbers 196/261, 480/978 is

GCF of Numerators i.e. for 196,480 is 4

LCM of denominators i.e. for 261,978 is 85086.

Thus, GCF of Fractions is 4/85086.Finally, GCF of Fractions for 196/261, 480/978 is 4/85086.