How to Find GCF of 300/470, 353/624?

GCF of 300/470, 353/624

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 300/470, 353/624 i.e 1/146640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/470, 353/624.

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 300/470,353/624?

Given fractions are 300/470,353/624

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 300/470,353/624, numerators are 300,353

Denominators are 470,624

The GCF of 300,353 is 1 .

LCM of 470,624 is 146640.

The greatest common factor of 300/470,353/624 = [GCF of 300,353]/[LCM of 470,624]= 1/146640

Therefore, the GCF of 300/470,353/624 is 1/146640.

Greatest Common Factor of 300,353

To find the highest common factor of 300,353, 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 353 are 1, 353

The HCF of 300,353 is 1.

Lets's calculate GCF of 300,353

Greatest Common Factor (GCF) of 300,353 By Common Division

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

Greatest Common Factor of 300,353 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 353

1,353

Greatest Common Factor

We found the factors 300,353 . The biggest common factor number is the GCF number.
So the greatest common factor 300,353 is 1.

Lets's calculate LCM of 470,624

Lowest Common Multiple of 470,624 using Common Division

2	470, 624
	235, 312

∴ So the LCM of the given numbers is 2 x 235 x 312 = 146640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/146640

Therefore, the GCF of Fractions 300/470,353/624 is 1/146640

Least Common Multiple of 470,624 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 470,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,624) = 2

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

GCF(470,624) x common factors =2 x 1 = 2

LCM(470,624) = ( 470 × 624 ) / 2

LCM(470,624) = 293280 / 2

LCM(470,624) = 146640

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FAQs on GCF of Fractions of 300/470, 353/624

1. What is the HCF of 300,353?

The HCF of 300,353 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 300/470, 353/624?

Answer: GCF of Numerators as per given numbers 300/470, 353/624 is

GCF of Numerators i.e. for 300,353 is 1

LCM of denominators i.e. for 470,624 is 146640.

Thus, GCF of Fractions is 1/146640.Finally, GCF of Fractions for 300/470, 353/624 is 1/146640.