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GCF of 514/32, 610/304

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 514/32, 610/304 i.e 2/608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/32, 610/304.

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 514/32,610/304?

Given fractions are 514/32,610/304

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 514/32,610/304, numerators are 514,610

Denominators are 32,304

The GCF of 514,610 is 2 .

LCM of 32,304 is 608.

The greatest common factor of 514/32,610/304 = [GCF of 514,610]/[LCM of 32,304]= 2/608

Therefore, the GCF of 514/32,610/304 is 2/608.

Greatest Common Factor of 514,610

To find the highest common factor of 514,610, we have to find the factors of both numbers and list the highest common factor.

The factors of 514 are 1, 2, 257, 514

The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The HCF of 514,610 is 2.

Lets's calculate GCF of 514,610

Greatest Common Factor (GCF) of 514,610 By Common Division

2 514, 610
257, 305

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

Greatest Common Factor of 514,610 By Matching Biggest Common Factor Method

Greatest Common Factor of 514,610 By Matching Biggest Common Factor Method

Now, list down the factors of 514

:

1,2,257,514

Now, list down the factors of 610

:

1,2,5,10,61,122,305,610

Greatest Common Factor

We found the factors 514,610 . The biggest common factor number is the GCF number.
So the greatest common factor 514,610 is 2.

Lets's calculate LCM of 32,304

Lowest Common Multiple of 32,304 using Common Division

2 32, 304
2 16, 152
2 8, 76
2 4, 38
2, 19

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 19 = 608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/608

Therefore, the GCF of Fractions 514/32,610/304 is 2/608

Least Common Multiple of 32,304 with GCF Formula

Least Common Multiple of 32,304 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 32,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,304) = 16

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

GCF(32,304) x common factors =16 x 1 = 16

LCM(32,304) = ( 32 × 304 ) / 16

LCM(32,304) = 9728 / 16

LCM(32,304) = 608


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FAQs on GCF of Fractions of 514/32, 610/304

1. What is the HCF of 514,610?

The HCF of 514,610 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 514/32, 610/304?

Answer: GCF of Numerators as per given numbers 514/32, 610/304 is

GCF of Numerators i.e. for 514,610 is 2

LCM of denominators i.e. for 32,304 is 608.

Thus, GCF of Fractions is 2/608.Finally, GCF of Fractions for 514/32, 610/304 is 2/608.