How to Find GCF of 900/543, 1695/227?

GCF of 900/543, 1695/227

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 900/543, 1695/227 i.e 15/123261 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/543, 1695/227.

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 900/543,1695/227?

Given fractions are 900/543,1695/227

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 900/543,1695/227, numerators are 900,1695

Denominators are 543,227

The GCF of 900,1695 is 15 .

LCM of 543,227 is 123261.

The greatest common factor of 900/543,1695/227 = [GCF of 900,1695]/[LCM of 543,227]= 15/123261

Therefore, the GCF of 900/543,1695/227 is 15/123261.

Greatest Common Factor of 900,1695

To find the highest common factor of 900,1695, we have to find the factors of both numbers and list the highest common factor.

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

The factors of 1695 are 1, 3, 5, 15, 113, 339, 565, 1695

The HCF of 900,1695 is 15.

Lets's calculate GCF of 900,1695

Greatest Common Factor (GCF) of 900,1695 By Common Division

3	900, 1695
5	300, 565
	60, 113

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 900,1695 By Matching Biggest Common Factor Method

Now, list down the factors of 900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

Now, list down the factors of 1695

1,3,5,15,113,339,565,1695

Greatest Common Factor

We found the factors 900,1695 . The biggest common factor number is the GCF number.
So the greatest common factor 900,1695 is 15.

Lets's calculate LCM of 543,227

Lowest Common Multiple of 543,227 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 123261

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/123261

Therefore, the GCF of Fractions 900/543,1695/227 is 15/123261

Least Common Multiple of 543,227 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 543,227 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(543,227) = 1

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

GCF(543,227) x common factors =1 x 1 = 1

LCM(543,227) = ( 543 × 227 ) / 1

LCM(543,227) = 123261 / 1

LCM(543,227) = 123261

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FAQs on GCF of Fractions of 900/543, 1695/227

1. What is the HCF of 900,1695?

The HCF of 900,1695 is 15

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 900/543, 1695/227?

Answer: GCF of Numerators as per given numbers 900/543, 1695/227 is

GCF of Numerators i.e. for 900,1695 is 15

LCM of denominators i.e. for 543,227 is 123261.

Thus, GCF of Fractions is 15/123261.Finally, GCF of Fractions for 900/543, 1695/227 is 15/123261.