How to Find GCF of 306/200, 8454/484?

GCF of 306/200, 8454/484

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 306/200, 8454/484 i.e 6/24200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/200, 8454/484.

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 306/200,8454/484?

Given fractions are 306/200,8454/484

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 306/200,8454/484, numerators are 306,8454

Denominators are 200,484

The GCF of 306,8454 is 6 .

LCM of 200,484 is 24200.

The greatest common factor of 306/200,8454/484 = [GCF of 306,8454]/[LCM of 200,484]= 6/24200

Therefore, the GCF of 306/200,8454/484 is 6/24200.

Greatest Common Factor of 306,8454

To find the highest common factor of 306,8454, we have to find the factors of both numbers and list the highest common factor.

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

The factors of 8454 are 1, 2, 3, 6, 1409, 2818, 4227, 8454

The HCF of 306,8454 is 6.

Lets's calculate GCF of 306,8454

Greatest Common Factor (GCF) of 306,8454 By Common Division

2	306, 8454
3	153, 4227
	51, 1409

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 306,8454 By Matching Biggest Common Factor Method

Now, list down the factors of 306

1,2,3,6,9,17,18,34,51,102,153,306

Now, list down the factors of 8454

1,2,3,6,1409,2818,4227,8454

Greatest Common Factor

We found the factors 306,8454 . The biggest common factor number is the GCF number.
So the greatest common factor 306,8454 is 6.

Lets's calculate LCM of 200,484

Lowest Common Multiple of 200,484 using Common Division

2	200, 484
2	100, 242
	50, 121

∴ So the LCM of the given numbers is 2 x 2 x 50 x 121 = 24200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/24200

Therefore, the GCF of Fractions 306/200,8454/484 is 6/24200

Least Common Multiple of 200,484 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 200,484 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(200,484) = 4

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

GCF(200,484) x common factors =4 x 1 = 4

LCM(200,484) = ( 200 × 484 ) / 4

LCM(200,484) = 96800 / 4

LCM(200,484) = 24200

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FAQs on GCF of Fractions of 306/200, 8454/484

1. What is the HCF of 306,8454?

The HCF of 306,8454 is 6

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 306/200, 8454/484?

Answer: GCF of Numerators as per given numbers 306/200, 8454/484 is

GCF of Numerators i.e. for 306,8454 is 6

LCM of denominators i.e. for 200,484 is 24200.

Thus, GCF of Fractions is 6/24200.Finally, GCF of Fractions for 306/200, 8454/484 is 6/24200.