How to Find GCF of 726/724, 300/742?

GCF of 726/724, 300/742

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 726/724, 300/742 i.e 6/268604 easily. The following is the detailed procedure to determine the greatest common factor of fractions 726/724, 300/742.

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 726/724,300/742?

Given fractions are 726/724,300/742

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 726/724,300/742, numerators are 726,300

Denominators are 724,742

The GCF of 726,300 is 6 .

LCM of 724,742 is 268604.

The greatest common factor of 726/724,300/742 = [GCF of 726,300]/[LCM of 724,742]= 6/268604

Therefore, the GCF of 726/724,300/742 is 6/268604.

Greatest Common Factor of 726,300

To find the highest common factor of 726,300, we have to find the factors of both numbers and list the highest common factor.

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726

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

The HCF of 726,300 is 6.

Lets's calculate GCF of 726,300

Greatest Common Factor (GCF) of 726,300 By Common Division

2	726, 300
3	363, 150
	121, 50

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 726,300 By Matching Biggest Common Factor Method

Now, list down the factors of 726

1,2,3,6,11,22,33,66,121,242,363,726

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

Greatest Common Factor

We found the factors 726,300 . The biggest common factor number is the GCF number.
So the greatest common factor 726,300 is 6.

Lets's calculate LCM of 724,742

Lowest Common Multiple of 724,742 using Common Division

2	724, 742
	362, 371

∴ So the LCM of the given numbers is 2 x 362 x 371 = 268604

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/268604

Therefore, the GCF of Fractions 726/724,300/742 is 6/268604

Least Common Multiple of 724,742 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 724,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(724,742) = 2

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

GCF(724,742) x common factors =2 x 1 = 2

LCM(724,742) = ( 724 × 742 ) / 2

LCM(724,742) = 537208 / 2

LCM(724,742) = 268604

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FAQs on GCF of Fractions of 726/724, 300/742

1. What is the HCF of 726,300?

The HCF of 726,300 is 6

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 726/724, 300/742?

Answer: GCF of Numerators as per given numbers 726/724, 300/742 is

GCF of Numerators i.e. for 726,300 is 6

LCM of denominators i.e. for 724,742 is 268604.

Thus, GCF of Fractions is 6/268604.Finally, GCF of Fractions for 726/724, 300/742 is 6/268604.