How to Find GCF of 300/679, 680/517?

GCF of 300/679, 680/517

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 300/679, 680/517 i.e 20/351043 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/679, 680/517.

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 300/679,680/517?

Given fractions are 300/679,680/517

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 300/679,680/517, numerators are 300,680

Denominators are 679,517

The GCF of 300,680 is 20 .

LCM of 679,517 is 351043.

The greatest common factor of 300/679,680/517 = [GCF of 300,680]/[LCM of 679,517]= 20/351043

Therefore, the GCF of 300/679,680/517 is 20/351043.

Greatest Common Factor of 300,680

To find the highest common factor of 300,680, we have to find the factors of both numbers and list the highest common factor.

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The HCF of 300,680 is 20.

Lets's calculate GCF of 300,680

Greatest Common Factor (GCF) of 300,680 By Common Division

2	300, 680
2	150, 340
5	75, 170
	15, 34

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 300,680 By Matching Biggest Common Factor Method

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Greatest Common Factor

We found the factors 300,680 . The biggest common factor number is the GCF number.
So the greatest common factor 300,680 is 20.

Lets's calculate LCM of 679,517

Lowest Common Multiple of 679,517 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 351043

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/351043

Therefore, the GCF of Fractions 300/679,680/517 is 20/351043

Least Common Multiple of 679,517 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 679,517 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(679,517) = 1

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

GCF(679,517) x common factors =1 x 1 = 1

LCM(679,517) = ( 679 × 517 ) / 1

LCM(679,517) = 351043 / 1

LCM(679,517) = 351043

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FAQs on GCF of Fractions of 300/679, 680/517

1. What is the HCF of 300,680?

The HCF of 300,680 is 20

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 300/679, 680/517?

Answer: GCF of Numerators as per given numbers 300/679, 680/517 is

GCF of Numerators i.e. for 300,680 is 20

LCM of denominators i.e. for 679,517 is 351043.

Thus, GCF of Fractions is 20/351043.Finally, GCF of Fractions for 300/679, 680/517 is 20/351043.