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GCF of 354/256, 306/350

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 354/256, 306/350 i.e 6/44800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/256, 306/350.

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 354/256,306/350?

Given fractions are 354/256,306/350

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 354/256,306/350, numerators are 354,306

Denominators are 256,350

The GCF of 354,306 is 6 .

LCM of 256,350 is 44800.

The greatest common factor of 354/256,306/350 = [GCF of 354,306]/[LCM of 256,350]= 6/44800

Therefore, the GCF of 354/256,306/350 is 6/44800.

Greatest Common Factor of 354,306

To find the highest common factor of 354,306, we have to find the factors of both numbers and list the highest common factor.

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354

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

The HCF of 354,306 is 6.

Lets's calculate GCF of 354,306

Greatest Common Factor (GCF) of 354,306 By Common Division

2 354, 306
3 177, 153
59, 51

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

Greatest Common Factor of 354,306 By Matching Biggest Common Factor Method

Greatest Common Factor of 354,306 By Matching Biggest Common Factor Method

Now, list down the factors of 354

:

1,2,3,6,59,118,177,354

Now, list down the factors of 306

:

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

Greatest Common Factor

We found the factors 354,306 . The biggest common factor number is the GCF number.
So the greatest common factor 354,306 is 6.


Lets's calculate LCM of 256,350

Lowest Common Multiple of 256,350 using Common Division

2 256, 350
128, 175

∴ So the LCM of the given numbers is 2 x 128 x 175 = 44800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/44800

Therefore, the GCF of Fractions 354/256,306/350 is 6/44800

Least Common Multiple of 256,350 with GCF Formula

Least Common Multiple of 256,350 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 256,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(256,350) = 2

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

GCF(256,350) x common factors =2 x 1 = 2

LCM(256,350) = ( 256 × 350 ) / 2

LCM(256,350) = 89600 / 2

LCM(256,350) = 44800


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 354/256, 306/350

1. What is the HCF of 354,306?

The HCF of 354,306 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 354/256, 306/350?

Answer: GCF of Numerators as per given numbers 354/256, 306/350 is

GCF of Numerators i.e. for 354,306 is 6

LCM of denominators i.e. for 256,350 is 44800.

Thus, GCF of Fractions is 6/44800.Finally, GCF of Fractions for 354/256, 306/350 is 6/44800.