How to Find GCF of 68/309, 13/208, 313/200?

GCF of 68/309, 13/208, 313/200

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 68/309, 13/208, 313/200 i.e 1/1606800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/309, 13/208, 313/200.

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 68/309,13/208,313/200?

Given fractions are 68/309,13/208,313/200

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 68/309,13/208,313/200, numerators are 68,13,313

Denominators are 309,208,200

The GCF of 68,13,313 is 1 .

LCM of 309,208,200 is 1606800.

The greatest common factor of 68/309,13/208,313/200 = [GCF of 68,13,313]/[LCM of 309,208,200]= 1/1606800

Therefore, the GCF of 68/309,13/208,313/200 is 1/1606800.

Greatest Common Factor of 68,13,313

To find the highest common factor of 68,13,313, we have to find the factors of both numbers and list the highest common factor.

The factors of 68 are 1, 2, 4, 17, 34, 68

The factors of 13 are 1, 13

The factors of 313 are 1, 313

The HCF of 68,13,313 is 1.

Lets's calculate GCF of 68,13,313

Greatest Common Factor (GCF) of 68,13,313 By Common Division

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

Greatest Common Factor of 68,13,313 By Matching Biggest Common Factor Method

Now, list down the factors of 68

1,2,4,17,34,68

Now, list down the factors of 13

1,13

Now, list down the factors of 313

1,313

Greatest Common Factor

We found the factors 68,13,313 . The biggest common factor number is the GCF number.
So the greatest common factor 68,13,313 is 1.

Lets's calculate LCM of 309,208,200

Lowest Common Multiple of 309,208,200 using Common Division

2	309, 208, 200
2	309, 104, 100
2	309, 52, 50
	309, 26, 25

∴ So the LCM of the given numbers is 2 x 2 x 2 x 309 x 26 x 25 = 1606800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1606800

Therefore, the GCF of Fractions 68/309,13/208,313/200 is 1/1606800

Least Common Multiple of 309,208,200 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 309,208,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(309,208,200) = 1

common factors(in case of two or more numbers have common factors) = 8

GCF(309,208,200) x common factors =1 x 8 = 8

LCM(309,208,200) = ( 309 × 208 × 200 ) / 8

LCM(309,208,200) = 12854400 / 8

LCM(309,208,200) = 1606800

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FAQs on GCF of Fractions of 68/309, 13/208, 313/200

1. What is the HCF of 68,13,313?

The HCF of 68,13,313 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 68/309, 13/208, 313/200?

Answer: GCF of Numerators as per given numbers 68/309, 13/208, 313/200 is

GCF of Numerators i.e. for 68,13,313 is 1

LCM of denominators i.e. for 309,208,200 is 1606800.

Thus, GCF of Fractions is 1/1606800.Finally, GCF of Fractions for 68/309, 13/208, 313/200 is 1/1606800.