How to Find GCF of 71/65, 54/304, 314/456?

GCF of 71/65, 54/304, 314/456

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 71/65, 54/304, 314/456 i.e 1/59280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/65, 54/304, 314/456.

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 71/65,54/304,314/456?

Given fractions are 71/65,54/304,314/456

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 71/65,54/304,314/456, numerators are 71,54,314

Denominators are 65,304,456

The GCF of 71,54,314 is 1 .

LCM of 65,304,456 is 59280.

The greatest common factor of 71/65,54/304,314/456 = [GCF of 71,54,314]/[LCM of 65,304,456]= 1/59280

Therefore, the GCF of 71/65,54/304,314/456 is 1/59280.

Greatest Common Factor of 71,54,314

To find the highest common factor of 71,54,314, we have to find the factors of both numbers and list the highest common factor.

The factors of 71 are 1, 71

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 314 are 1, 2, 157, 314

The HCF of 71,54,314 is 1.

Lets's calculate GCF of 71,54,314

Greatest Common Factor (GCF) of 71,54,314 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 71,54,314 By Matching Biggest Common Factor Method

Now, list down the factors of 71

1,71

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 314

1,2,157,314

Greatest Common Factor

We found the factors 71,54,314 . The biggest common factor number is the GCF number.
So the greatest common factor 71,54,314 is 1.

Lets's calculate LCM of 65,304,456

Lowest Common Multiple of 65,304,456 using Common Division

2	65, 304, 456
2	65, 152, 228
2	65, 76, 114
19	65, 38, 57
	65, 2, 3

∴ So the LCM of the given numbers is 2 x 2 x 2 x 19 x 65 x 2 x 3 = 59280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59280

Therefore, the GCF of Fractions 71/65,54/304,314/456 is 1/59280

Least Common Multiple of 65,304,456 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 65,304,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,304,456) = 1

common factors(in case of two or more numbers have common factors) = 152

GCF(65,304,456) x common factors =1 x 152 = 152

LCM(65,304,456) = ( 65 × 304 × 456 ) / 152

LCM(65,304,456) = 9010560 / 152

LCM(65,304,456) = 59280

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 71/65, 54/304, 314/456

1. What is the HCF of 71,54,314?

The HCF of 71,54,314 is 1

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 71/65, 54/304, 314/456?

Answer: GCF of Numerators as per given numbers 71/65, 54/304, 314/456 is

GCF of Numerators i.e. for 71,54,314 is 1

LCM of denominators i.e. for 65,304,456 is 59280.

Thus, GCF of Fractions is 1/59280.Finally, GCF of Fractions for 71/65, 54/304, 314/456 is 1/59280.