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GCF of 364/309, 206/278

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 364/309, 206/278 i.e 2/85902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/309, 206/278.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 364/309,206/278?

Given fractions are 364/309,206/278

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 364/309,206/278, numerators are 364,206

Denominators are 309,278

The GCF of 364,206 is 2 .

LCM of 309,278 is 85902.

The greatest common factor of 364/309,206/278 = [GCF of 364,206]/[LCM of 309,278]= 2/85902

Therefore, the GCF of 364/309,206/278 is 2/85902.

Greatest Common Factor of 364,206

To find the highest common factor of 364,206, we have to find the factors of both numbers and list the highest common factor.

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The factors of 206 are 1, 2, 103, 206

The HCF of 364,206 is 2.

Lets's calculate GCF of 364,206

Greatest Common Factor (GCF) of 364,206 By Common Division

2 364, 206
182, 103

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

Greatest Common Factor of 364,206 By Matching Biggest Common Factor Method

Greatest Common Factor of 364,206 By Matching Biggest Common Factor Method

Now, list down the factors of 364

:

1,2,4,7,13,14,26,28,52,91,182,364

Now, list down the factors of 206

:

1,2,103,206

Greatest Common Factor

We found the factors 364,206 . The biggest common factor number is the GCF number.
So the greatest common factor 364,206 is 2.

Lets's calculate LCM of 309,278

Lowest Common Multiple of 309,278 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 85902

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85902

Therefore, the GCF of Fractions 364/309,206/278 is 2/85902

Least Common Multiple of 309,278 with GCF Formula

Least Common Multiple of 309,278 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 309,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(309,278) = 1

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

GCF(309,278) x common factors =1 x 1 = 1

LCM(309,278) = ( 309 × 278 ) / 1

LCM(309,278) = 85902 / 1

LCM(309,278) = 85902


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FAQs on GCF of Fractions of 364/309, 206/278

1. What is the HCF of 364,206?

The HCF of 364,206 is 2

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 364/309, 206/278?

Answer: GCF of Numerators as per given numbers 364/309, 206/278 is

GCF of Numerators i.e. for 364,206 is 2

LCM of denominators i.e. for 309,278 is 85902.

Thus, GCF of Fractions is 2/85902.Finally, GCF of Fractions for 364/309, 206/278 is 2/85902.