How to Find GCF of 900/137, 340/242?

GCF of 900/137, 340/242

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 900/137, 340/242 i.e 20/33154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/137, 340/242.

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 900/137,340/242?

Given fractions are 900/137,340/242

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 900/137,340/242, numerators are 900,340

Denominators are 137,242

The GCF of 900,340 is 20 .

LCM of 137,242 is 33154.

The greatest common factor of 900/137,340/242 = [GCF of 900,340]/[LCM of 137,242]= 20/33154

Therefore, the GCF of 900/137,340/242 is 20/33154.

Greatest Common Factor of 900,340

To find the highest common factor of 900,340, 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 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

The HCF of 900,340 is 20.

Lets's calculate GCF of 900,340

Greatest Common Factor (GCF) of 900,340 By Common Division

2	900, 340
2	450, 170
5	225, 85
	45, 17

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

Greatest Common Factor of 900,340 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 340

1,2,4,5,10,17,20,34,68,85,170,340

Greatest Common Factor

We found the factors 900,340 . The biggest common factor number is the GCF number.
So the greatest common factor 900,340 is 20.

Lets's calculate LCM of 137,242

Lowest Common Multiple of 137,242 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 33154

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/33154

Therefore, the GCF of Fractions 900/137,340/242 is 20/33154

Least Common Multiple of 137,242 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 137,242 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(137,242) = 1

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

GCF(137,242) x common factors =1 x 1 = 1

LCM(137,242) = ( 137 × 242 ) / 1

LCM(137,242) = 33154 / 1

LCM(137,242) = 33154

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FAQs on GCF of Fractions of 900/137, 340/242

1. What is the HCF of 900,340?

The HCF of 900,340 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 900/137, 340/242?

Answer: GCF of Numerators as per given numbers 900/137, 340/242 is

GCF of Numerators i.e. for 900,340 is 20

LCM of denominators i.e. for 137,242 is 33154.

Thus, GCF of Fractions is 20/33154.Finally, GCF of Fractions for 900/137, 340/242 is 20/33154.