How to Find GCF of 300/728, 870/706?

GCF of 300/728, 870/706

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 300/728, 870/706 i.e 30/256984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/728, 870/706.

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 300/728,870/706?

Given fractions are 300/728,870/706

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 300/728,870/706, numerators are 300,870

Denominators are 728,706

The GCF of 300,870 is 30 .

LCM of 728,706 is 256984.

The greatest common factor of 300/728,870/706 = [GCF of 300,870]/[LCM of 728,706]= 30/256984

Therefore, the GCF of 300/728,870/706 is 30/256984.

Greatest Common Factor of 300,870

To find the highest common factor of 300,870, 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 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 300,870 is 30.

Lets's calculate GCF of 300,870

Greatest Common Factor (GCF) of 300,870 By Common Division

2	300, 870
3	150, 435
5	50, 145
	10, 29

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 300,870 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 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 300,870 . The biggest common factor number is the GCF number.
So the greatest common factor 300,870 is 30.

Lets's calculate LCM of 728,706

Lowest Common Multiple of 728,706 using Common Division

2	728, 706
	364, 353

∴ So the LCM of the given numbers is 2 x 364 x 353 = 256984

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/256984

Therefore, the GCF of Fractions 300/728,870/706 is 30/256984

Least Common Multiple of 728,706 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 728,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(728,706) = 2

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

GCF(728,706) x common factors =2 x 1 = 2

LCM(728,706) = ( 728 × 706 ) / 2

LCM(728,706) = 513968 / 2

LCM(728,706) = 256984

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FAQs on GCF of Fractions of 300/728, 870/706

1. What is the HCF of 300,870?

The HCF of 300,870 is 30

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 300/728, 870/706?

Answer: GCF of Numerators as per given numbers 300/728, 870/706 is

GCF of Numerators i.e. for 300,870 is 30

LCM of denominators i.e. for 728,706 is 256984.

Thus, GCF of Fractions is 30/256984.Finally, GCF of Fractions for 300/728, 870/706 is 30/256984.